ĐĎॹá>ţ˙ řŚţ˙˙˙ Ą˘üű€€ní€űúů˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙ěĽÁ5@ řż0ćübjbjĎ2Ď2  .­X­Xô’;˙˙˙˙˙˙ˆŠŠŠ4žć ć ć hN´Lžč|˜Zž4Ld4d4Œ4!>2S>g> v v v v)IvYyi|$€Rҁ¤|ŠAy<¨!>AA|d4Œ4í˘|ÖOÖOÖOArRd4(ŠŒ4vÖOAvÖOPÖO&QňŸlh"ŠrqŒ4N pCl@’˜Ăć zB‚ śoN"rü¸|0č|pnv‚üNŹv‚œrqžžv‚Šrq°s>’?hÖOm?TÁ?Gs>s>s>||žž¤•bš„s¨O.žžbš LOCAL LINEARITY: SEEING MAY BE BELIEVING A function f is said to be linear over an interval if the difference quotient  EMBED Equation  is constant over that interval. Although few functions (other than linear functions) are linear over an interval, all functions that are differentiable at some point where x =c are well-modeled by a unique tangent line in a neighborhood of c and are thus considered locally linear. Local linearity is an extremely powerful and fertile concept. Most students feel comfortable finding or identifying the slope of a linear function. Most students understand that a linear function has a constant slope. Our goal should be to build on this knowledge and to help students understand that most of the functions they will encounter are "nearly linear" over very small intervals; that is most functions are locally linear. Thus, when we "zoom in" on a point on the graph of a function, we are very likely to "see" what appears to be a straight line. Even more important, we want them to understand the powerful implications of this fact! The Derivative If shown the following graph and asked to write the rule, most students will write f(x) = x. This shows some good understanding, but not enough skepticism.  If the viewing window [-.29,.29] x [-.19,.19] were known, some students might actually question whether enough is known to conjecture about the function presented. In the viewing window [-4,4] x [-2,2], a very different graph is observed:  As teachers, we understand that the first window gets at the idea of local linearity (in the neighborhood of x = 0) of the differentiable function we see in the second window. In fact, the two windows are also supportive of an important limit result:  EMBED Equation.2 ! Our ultimate goal, however, is to have students come upon at least an intuitive understanding of the formal definition of the derivative of a function f for themselves. They should be able to say "of course" rather than question "What IS that?" when presented with that formal definition. It is technology that makes this approach possible, and that helps students understand the concept of derivative rather than merely memorizing some obscure (to them) notation. Technology to the Rescue: Discovering local linearity of common functions Start with a simple non-linear function, say  EMBED Equation.DSMT4 . Select an integer x-value and have students “zoom-in” on that point on the graph until they “see” a line in their viewing window. Ask them to use some method to estimate the slope of the “line” and be ready to describe their process. Most will pick two nearby points and use the slope formula. If they have done as instructed, they should all be finding a slope value very nearly the same. If not, ask them to work in small groups until everyone has agreed on some common reasonable estimate. This will allow them to check their method and become comfortable with the technology. Next, assign pairs of students their own, personal x-coordinate. In fact, if the class is small, you might assign two or more x-coordinates to each pair. Be sure the assign both positive and negative x-coordinates within an interval, say [-4,4]. Most of the assigned values will be given in tenths. Make a table of results (either on the board or using the statistics capabilities of your overhead calculator). The class should discover on their own that there appears to be a predictable relationship between the x-coordinate and the resulting slope. In fact, they are likely to make a conjecture about the general derivative function without even realizing what they are doing. This conjecture can be confirmed using the difference quotient and an intuitive idea of limit as follows: If a student group was assigned the x-value of  EMBED Equation.DSMT4 , then they would have predicted the slope of a line containing the point  EMBED Equation.DSMT4 . When they zoomed in, a nearby coordinate might have been (x, x2). Thus, their predicted slope would have been  EMBED Equation.DSMT4  which can be easily simplified to  EMBED Equation.DSMT4 . If x is “very close” to  EMBED Equation.DSMT4  in value, then the predicted slope should have almost  EMBED Equation.DSMT4 ! Linear Approximation In the Pre-technological Age, linear approximation was a useful evaluation tool. To students today, it may seem like a historic lodestone around their neck. They can just imagine a teacher thinking, "I had to do this, so you will too!" This topic should be presented as a first (and perhaps primitive step) toward what we know as Taylor Polynomials. In fact, many of us may decide to acquaint our AB as well as BC students with the idea of quadratic or cubic approximations as well. Whether we do so or not, the notion of using lines to model the behavior of a function in a small neighborhood of some domain value at which the function is differentiable, should be clear to those students who have developed the concept of local linearity. Within the following actual free response questions, we find many applications of local linearity that should “be obvious” to students who truly understand the derivative of a function at a particular point. 1998 AB4 Let  EMBED Equation  be a function with  EMBED Equation  such that for all points  EMBED Equation  on the graph of  EMBED Equation  the slope is given by  EMBED Equation . Find the slope of the graph of  EMBED Equation  at the point where  EMBED Equation . Write an equation for the line tangent to the graph of  EMBED Equation  at  EMBED Equation  and use it to approximate  EMBED Equation . Find  EMBED Equation  by solving the separable differential equation  EMBED Equation  with the initial condition  EMBED Equation . Use your solution from part (c) to find  EMBED Equation . Instantaneous Rate of Change The new course description includes "instantaneous rate of change as the limit of average rate of change.” Many students find it helpful to understand instantaneous rate as what a policeman's radar gun approximates. The radar gun actually reads two positions of the vehicle over an extremely small interval of time and generates the average rate of change on that tiny interval of time. Thus local linearity once again comes to the rescue and allows us to model the situation in such a way as to help us (and the policeman) see a constant rate where there may be none. The definition of instantaneous rate of change becomes obvious. 1998 - AB 3  The graph of the velocity  EMBED Equation , in  EMBED Equation , of a car traveling on a straight road, for  EMBED Equation , is shown above. A table of values for  EMBED Equation , at 5 second intervals of time t, is shown to the right of the graph. (a) During what intervals of time is the acceleration of the car positive? Give a reason for your answer. (b) Find the average acceleration of the car, in  EMBED Equation , over the interval  EMBED Equation . (c) Find one approximation for the acceleration of the car, in  EMBED Equation , at  EMBED Equation . Show the computations you used to arrive at your answer. Approximate  EMBED Equation  with a Riemann sum, using the midpoints of five subintervals of equal length. Using correct units, explain the meaning of this integral. Differential Equations and Slope Fields The AB and BC syllabi now include finding solutions of variable separable differential equations, and we will come back to this topic later. Effective with the 2004 Examinations, the topic of slope fields (now only in the BC syllabus) will become a part of the AB syllabus. We can begin to set the stage for a more thorough look at slope fields and differential equations early in the year. A Slope field (sometimes called a directional field) is used to give us insight into the graphical behavior of a function by looking at its rate of change (derivative) function. For example, consider the differential equation given by  EMBED Equation.DSMT4 . That is, for some function  EMBED Equation.DSMT4 , y is changing (with respect to x) at a rate that is directly proportional to x itself, and the constant of proportionality is 2. Suppose we know that  EMBED Equation.DSMT4 . We could use the fact that for  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  to find that the slope of  EMBED Equation.DSMT4  at x = 1 is 2. We could then write the equation for the line tangent to the graph of  EMBED Equation.DSMT4  at x = 1 as  EMBED Equation.DSMT4 . In fact, we could graph a small piece of the line tangent to  EMBED Equation.DSMT4  at (1,4) and “see” the behavior of  EMBED Equation.DSMT4  near this point.  Of course, we know that  EMBED Equation.DSMT4  is not linear because its rate of change function is not constant, but we get a glimpse of  EMBED Equation.DSMT4  based on local linearity. Given ONLY the differential equation  EMBED Equation.DSMT4 , we do not know particular values of  EMBED Equation.DSMT4 , but we can “see” the behavior of the graph by creating an entire slope field . First, complete the table below for this differential equation. x EMBED Equation.DSMT4 -3-2-10123 Next, transfer the information above to the grid below showing little portions of the tangent line at each of the indicated points. After doing so, can you begin the get a sense of the family of functions  EMBED Equation.DSMT4  whose derivative is  EMBED Equation.DSMT4 ?  We will return to the exploration of slope fields later, but for now, notice that here is just one more powerful application of local linearity! Definitive? Definitions Definition: Let a function  EMBED Equation.DSMT4  be defined on some interval I. We say that f is increasing on I provided that for all  EMBED Equation.DSMT4 , if  EMBED Equation.DSMT4  , then  EMBED Equation.DSMT4 . Properties contributed by Theorems of Calculus: If  EMBED Equation.DSMT4  for all  EMBED Equation.DSMT4 , then  EMBED Equation.DSMT4  is increasing on I. Note: This theorem of calculus does not say that  EMBED Equation.DSMT4  is a requirement for  EMBED Equation.DSMT4  to be increasing on I. The theorem only speaks to what happens if  EMBED Equation.DSMT4 . Another way to look at this is that the inverse of a conditional statement is not necessarily true. If  EMBED Equation.DSMT4  at each point  EMBED Equation.DSMT4  and if  EMBED Equation.DSMT4  is continuous on  EMBED Equation.DSMT4  and differentiable on  EMBED Equation.DSMT4 , then  EMBED Equation.DSMT4  is increasing on  EMBED Equation.DSMT4 . Clarifying Examples: Given  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4  increases on  EMBED Equation.DSMT4  even though  EMBED Equation.DSMT4 . Given  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4  increases on  EMBED Equation.DSMT4 and on  EMBED Equation.DSMT4 . Note: Many textbooks/mathematicians say that this function  EMBED Equation.DSMT4  “is an increasing function” (meaning that  EMBED Equation.DSMT4 increases on its discrete domain intervals). However, the domain for this function is  EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4 , and  EMBED Equation.DSMT4 is not increasing on its domain. Given the following function  EMBED Equation.DSMT4   EMBED MSDraw.Drawing.8.2   EMBED Equation.DSMT4  increase on  EMBED Equation.DSMT4  even though  EMBED Equation.DSMT4  does not exist. Given  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4  decreases on  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  increases on  EMBED Equation.DSMT4 . Note:  EMBED Equation.DSMT4  is decreasing at each point of  EMBED Equation.DSMT4  and increasing at each point of  EMBED Equation.DSMT4 . The function  EMBED Equation.DSMT4  is neither increasing nor decreasing at  EMBED Equation.DSMT4  because there is no open interval contain  EMBED Equation.DSMT4  for which  EMBED Equation.DSMT4  for all x in that interval. This points out the difference between intervals over which a function increases and points at which a function is increasing. Definition: Let  EMBED Equation.DSMT4  be a function that is differentiable on an open interval  EMBED Equation.DSMT4 . We say that the graph of  EMBED Equation.DSMT4  is concave up on  EMBED Equation.DSMT4  if  EMBED Equation.DSMT4  is increasing on  EMBED Equation.DSMT4 . Properties contributed by Theorems of Calculus: If  EMBED Equation.DSMT4  for all  EMBED Equation.DSMT4 , then the graph of  EMBED Equation.DSMT4  is concave up on  EMBED Equation.DSMT4 . If  EMBED Equation.DSMT4  and if  EMBED Equation.DSMT4 , then there is a local minimum at  EMBED Equation.DSMT4 . Note: This is often referred to as the Second derivative Test for Local Extrema. Note: Based upon the definition above, it is correct to say that “ EMBED Equation.DSMT4  is concave up on any open interval over which  EMBED Equation.DSMT4  for all x belonging to that interval”, but it is not correct to say that that “ EMBED Equation.DSMT4  is concave up only on an open interval over which for all x belonging to that interval”. Clarifying Examples Based Upon the Definition Above: Given  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4 is concave up on  EMBED Equation.DSMT4  even though  EMBED Equation.DSMT4 . This is true because  EMBED Equation.DSMT4  and thus  EMBED Equation.DSMT4  is increasing on  EMBED Equation.DSMT4 . Given  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4 is concave up on  EMBED Equation.DSMT4  and concave down on  EMBED Equation.DSMT4 . The endpoints at  EMBED Equation.DSMT4  are not included because the definition addresses concavity only on an open interval. Given  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4 is concave up on  EMBED Equation.DSMT4  and concave up on  EMBED Equation.DSMT4 . It is not concave up on  EMBED Equation.DSMT4  because  EMBED Equation.DSMT4  is not differentiable at  EMBED Equation.DSMT4 . Definition One: A point of inflection is a point at which the graph of  EMBED Equation.DSMT4  is continuous and at which  EMBED Equation.DSMT4  changes sign. Definition Two: A point of inflection is a point at which the graph of  EMBED Equation.DSMT4  has a tangent line and at which  EMBED Equation.DSMT4  changes sign. Note: Mathematicians choose to disagree as to whether a tangent line is required or not. Clarifying Examples: Given  EMBED Equation.DSMT4 ; the graph of f has a point of inflection at (0,0) by either definition. Although  EMBED Equation.DSMT4  is not defined at  EMBED Equation.DSMT4 , there is a best linear model (a.k.a. tangent line) at this point – the vertical line  EMBED Equation.DSMT4 . Given  EMBED Equation.DSMT4 ; the graph of f has a point of inflection at (2,3) by Definition One because the graph of f is continuous and changes concavity there. However, the graph of f does not have a point of inflection at (2,3) by Definition Two because the graph of f has a cusp at (2,3) and thus does not have a tangent line at that point. Given  EMBED Equation.DSMT4 ; the graph of f does not have a point of inflection at (0,0) by either definition. Although  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  does not have a change of sign around the origin. What Does a Respected Mathematics Dictionary Say? Mathematical Dictionary, 5th Edition by James and James provides the following as definitions. Increasing Function: If a function f is differentiable on an open interval I, then the function is increasing on I if the derivative is non-negative throughout I and not identically zero in any interval of I. Note: This is sufficient, but not necessary (see example 3 in the increasing function discussion.) Concave Up: A curve is concave toward a line if every segment of the arc cut off by a chord lies in the chord or on the opposite side of the chord from the line. If the line is horizontal such that the curve lies below it and is concave toward it, the curve is said to be concave up. Note: If you think this is tough to understand (much less, apply), you’re not alone. It might be paraphrased to say that the graph of a function is concave up on an interval  EMBED Equation.DSMT4  if the graph always lies below a segment joining any two points of the graph on that interval. This would still be a horrendous definition to apply. What Do Some Textbooks Use as Definitions? Calculus: Graphical Numerical, Algebraic by Finney, Demana, Waits, Kennedy 1999 says Increasing Function: Let f be a function defined on an interval I. Then f increases on I if, for any two points  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  in I,  EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4 . Concave Up: The graph of a differentiable function  EMBED Equation.DSMT4  is concave up on an interval I if  EMBED Equation.DSMT4  is increasing on I. Point of Inflection: A point where the graph of a function has a tangent line and where the concavity changes is a point of inflection. Calculus, Single Variable , 2nd ed. by Hughes Hallett, Gleason, et al. 1992 says Increasing Function: A function f is increasing if the values of  EMBED Equation.DSMT4  increase as x increases. Concave Up: If  EMBED Equation.DSMT4 >0 on an interval, then  EMBED Equation.DSMT4  is increasing, so the graph of  EMBED Equation.DSMT4  is concave up there. Inflection Point: A point at which the function changes concavity is called a point of inflection. Calculus 5th ed.by Larson, Hostetler, Evans says Increasing Function: A function f is increasing on an interval if for any two numbers  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  in the interval,  EMBED Equation.DSMT4  implies  EMBED Equation.DSMT4 . Concave Up: Let f be differentiable on an open interval, I. The graph of f is concave upward on I if  EMBED Equation.DSMT4  is increasing on the interval. Point of Inflection: If the concavity of f changes at a point for which a tangent line to the graph exists, then the point is a point of inflection. Calculus 4th ed. by Stewart 1999 says Increasing Function: A function is called increasing on an interval I if  EMBED Equation.DSMT4  whenever  EMBED Equation.DSMT4  in I. Concave Up: If the graph of f lies above all of its tangents on an interval I, then it is called concave upward on I. Point of Inflection: A point P on a curve is called an inflection point if the curve changes concavity at P. Calculus 5th ed by Anton 1995 says Increasing Function: Let f be defined on an interval, and let x1 and x2 denote points in that interval. The function f is increasing on the interval if  EMBED Equation.DSMT4  whenever  EMBED Equation.DSMT4 . Concave Up: Let f be differentiable on an interval. The function f is called concave up on the interval if  EMBED Equation.DSMT4  is increasing on the interval Point of Inflection: If f is continuous on an open interval containing xo, and if f changes direction of its concavity at xo, then the point  EMBED Equation.DSMT4  on the graph is called an inflection point of f. RULES TO DIFFERENTIATE BY In the Age of Computer programs such as Maple and Derive , Hewlett Packard’s and TI-89’s, and other high power technology, should we require our students to know and to be able to apply the rules of differentiation? Most of us would really like to answer “yes” but is there just cause to do so (not just the old “we had to learn the rules therefore so do you” response?) Ties that Bind (Local Linearity Revisited) A function that is differentiable at  EMBED Equation  possesses a unique best linear model (known as the tangent line) at that point. This property prompts an understanding of the “logic” behind many of our rules of differentiation. I . Consider two functions,  EMBED Equation  and  EMBED Equation , that are differentiable at  EMBED Equation . Let  EMBED Equation . What does local linearity at  EMBED Equation  contribute to our understanding about why it is that  EMBED Equation ? II. Consider a function  EMBED Equation  that is differentiable at  EMBED Equation . Let  EMBED Equation  where  EMBED Equation  is a non-zero constant. What does local linearity at  EMBED Equation  contribute to our understanding about why it is that  EMBED Equation ? III. Consider two functions,  EMBED Equation  and  EMBED Equation , that are differentiable at  EMBED Equation . Let  EMBED Equation . What does local linearity at  EMBED Equation  contribute to our understanding about why it is that  EMBED Equation ? Is there anything that local linearity or previous mathematics contributes to our understanding about why it is that  EMBED Equation ? The Chain Rule Once students have learned how to differentiate some basic functions, there are fun and interesting ways for them to “discover” the Chain Rule. The following are several good functions with which to start the exploration:  EMBED Equation   EMBED Equation   EMBED Equation   EMBED Equation   EMBED Equation  A step toward confirming conjectures that arise from exploration of the Chain Rule Consider two functions,  EMBED Equation  and  EMBED Equation , that are differentiable at  EMBED Equation . Let  EMBED Equation . What does local linearity at  EMBED Equation  contribute to our understanding about why it is that  EMBED Equation ? Assessing Student Ability to Apply the Rules of Differentiation 1977 AB4, BC2 Let f and g and their inverses f-1 and g-1 be differentiable functions and let the values of f, g, and the derivatives f' and g' at x=1 and x=2 be given by the table below. xf(x)g(x)f '(x)g '(x)1325422 EMBED Equation.2 67 Determine the value of each of the following (a) The derivative of f+g at x=2 (b) The derivative of fg at x=2 (c) The derivative of f/g at x=2 (d) h'(1) where h(x) = f(g(x)) (e) The derivative of g-1 at x=2 A Variation on the Theme Given that f and g are both differentiable functions on the interval (-10,10) and specific values of the functions and their derivatives are provided in the table below. xf(x)f ' (x)g(x)g ' (x)-147-523-23-1 EMBED Equation.2  (a) Find p '(3) if P(x) = f(x) g(x) (b) Find s ' (-1) if s(x) = f(x) + p(x) (c) Find q ' (x) if q(x) = f(x) / g(x) (d) Find c ' (3) if c(x) = f(g(x)) (e) Find the slope of g-1 (x) at x = -1 if g-1 represents the inverse function of g (f) Find h ' ( EMBED Equation.2 ) if h(x) = f(x2) Questions from other sources: From Calculus 3rd Edition by Stewart If  EMBED Equation  where  EMBED Equation  is differentiable at  EMBED Equation , find  EMBED Equation , Suppose  EMBED Equation  is a differentiable function such that  EMBED Equation . If  EMBED Equation , evaluate  EMBED Equation . From Calculus, 5th Edition by Anton Given the following table of values, find the requested derivatives. x EMBED Equation  EMBED Equation 21785- 3  EMBED Equation  where  EMBED Equation   EMBED Equation  where  EMBED Equation  Given that  EMBED Equation  and  EMBED Equation , find  EMBED Equation  if  EMBED Equation  Find  EMBED Equation  if  EMBED Equation . From Calculus 3rd Edition by Gillett Suppose that  EMBED Equation . Confirm that  EMBED Equation  Why is it incorrect to say that  EMBED Equation ? Over what intervals is  EMBED Equation  Explain why the range of  EMBED Equation  is  EMBED Equation  Let  EMBED Equation  and  EMBED Equation . Use the definition of the derivative to show that  EMBED Equation  and that  EMBED Equation . If  EMBED Equation  and we attempt to evaluate  EMBED Equation , what goes wrong? Does  EMBED Equation ? (This problem illustrates how one-sided derivatives can complicate the theory. Rather than stating hypotheses that exclude such cases, we assume that algebraic combinations of functions are legitimate only when the domains overlap in nontrivial ways.) from Calculus Problems for a New Century, MAA Notes Number 28 Let  EMBED Equation  where the graphs of  EMBED Equation  and  EMBED Equation  are given below. Evaluate  EMBED Equation . Estimate  EMBED Equation  Let  EMBED Equation  where the graphs of  EMBED Equation  and  EMBED Equation  are given below. (a) Is  EMBED Equation  positive, negative, or zero. Explain how you know. (b) Is  EMBED Equation  positive, negative, or zero. Explain how you know. (c) *** Estimate the value of  EMBED Equation  IMPLICIT DIFFERENTIATION and RELATED RATES Many functions that our students and we encounter can be described by explicitly expressing one variable in terms of another. After exploring the Chain Rule, however, it is possible to work with functions that are defined implicitly by a relation between x and y. The classic introductory example of implicitly defined functions in most textbooks is  EMBED Equation . This example illustrates a situation where two functions are defined by the given relationship – one is the upper branch of a circle and the other is the lower branch of that same circle. Let’s consider those two functions, namely  EMBED Equation  and  EMBED Equation . Given that  EMBED Equation , it is simple to show that both  EMBED Equation  and  EMBED Equation  satisfy the given relationship. For example,  EMBED Equation  because  EMBED Equation . The problem, which for the most part is beyond the scope of a first year Calculus course, is that not all relations define a function. In other words, there might not be a function that satisfies a given relation. A simple example of such a relation would be  EMBED Equation , a relation that is temptingly like the introductory relation of most texts. If one is too hasty, one will apply the procedure used to find the derivative of implicitly defined function, and arrive at an “answer”. However, by more careful inspection, one will note that the relation defined by  EMBED Equation  leads to the equivalent statement requiring  EMBED Equation . Oops! There is, in fact, an Implicit Function Theorem which tells us when a relation in  EMBED Equation  and  EMBED Equation  does define a differentiable function of  EMBED Equation . The statement and proof can be found in multivariable calculus textbooks, and depends upon an understanding of partial derivatives. Neither the statement nor the proof is within the grasp of most first year calculus students. Thus, the heart of the matter is that, as one honest author named Philip Gillett wrote to students, “We ask you to wait for a multivariable calculus; meanwhile you will have to trust us not to present any foolish problems.” Even though they are more than willing to trust teachers and textbook authors, many students find the concept of implicit differentiation perplexing. In this presentation, we will discuss ways to help students achieve greater understanding of the concepts that underlie implicit differentiation and attain greater confidence in their ability to correctly apply the procedure. If students understand the Chain Rule and implicit differentiation, then they will also better understand Related Rates problems. After some introductory discussion and work that will be detailed in the presentation, the following concept reinforcing-and-extending problems could be addressed. Assuming that the equation  EMBED Equation  defines one or more differentiable functions of the form  EMBED Equation , write an expression for  EMBED Equation . (1992 AB4, BC1) Consider the curve defined by the equation  EMBED Equation  for  EMBED Equation . Find  EMBED Equation  in terms of  EMBED Equation . Write an equation for each vertical tangent to the graph. Find  EMBED Equation  in terms of  EMBED Equation . (1980 AB6, BC4) Let  EMBED Equation  be the continuous function that satisfies the equation  EMBED Equation  and whose graph contains the points (2,1) and (-2,-2). Let  EMBED Equation  be the line tangent to the graph of  EMBED Equation at  EMBED Equation . Find an expression for  EMBED Equation . Write an equation for line  EMBED Equation . Give the coordinates of a point that is on the graph of  EMBED Equation  but is not on line  EMBED Equation . Give the coordinates of a point that is on line  EMBED Equation  but is not on the graph of  EMBED Equation . An icicle is in the shape of a right circular cone. At a particular moment in time the height is 15 cm and is increasing at the rate of 1 cm/hr, while the radius of the base is 2 cm and is decreasing at the rate of 0.1 cm/hr. Is the volume of ice increasing or decreasing at that instant? at what rate? 1995 AB5/BC3  As shown in the figure above, water is draining from a conical tank with height 12 feet and diameter 8 feet into a cylindrical tank that has a base with area EMBED EQUATION  square feet. The depth h, in feet, of the water in the conical tank is changing at the rate of EMBED EQUATION  feet per minute. (The volume V of a cone with radius r and height h is EMBED EQUATION .) (a) Write an expression for the volume of water in the conical tank as a function of h. (b) At what rate is the volume of water in the conical tank changing when EMBED EQUATION ? Indicate units of measure. (c) Let y be the depth, in feet, of the water in the cylindrical tank. At what rate is y changing when EMBED EQUATION ? Indicate units of measure. 6. 1991 AB6  A tightrope is stretched 30 feet above the ground between the Jay and the Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A, as shown in the diagram. (a) How fast is the shadow of the tightrope walker's feet moving along the ground when she is midway between the buildings? (Indicate units of measure.) (b) How far from point A is the tightrope walker when the shadow of her feet reaches the base of the Tee Building? (Indicate units of measure.) (c) How fast is the shadow of the tightrope walker's feet moving up the wall of the Tee building when she is 10 feet from point B ? (Indicate units of measure.) RELATING THE GRAPHS OF  EMBED Equation.3  In the past, our emphasis with students has been on the process of “finding” derivatives. We drilled our students on the various derivative rules; the rules became the focus until we turned to application problems. In the Age of Reform, however, we realize that we want our students to understand the concept of derivative better. We will hopefully spend less time in the future drilling students on rules, and more time on helping students develop an understanding of the concept of derivative. Gaining Information about the Slope of a Function from the Graph of that Function.  Example 1: Function F is defined and continuous on the closed interval [a,g]. The graph of F is shown above. Use this graph to answer the following questions. Over what intervals is F increasing ? Over what intervals is  EMBED Equation.DSMT4  > 0 ? At what x-values is  EMBED Equation.DSMT4  = 0 ? Example 2:  The graph of  EMBED Equation.DSMT4  , the derivative function for F, is sketched above.  EMBED Equation.DSMT4 is continuous on the interval (a,g). Use this graph to answer the following questions. (a) Over what interval(s) is  EMBED Equation.DSMT4 > 0 ? Over what interval(s) is  EMBED Equation.DSMT4 increasing ? Over what interval(s) is F increasing ? Over what interval(s) is  EMBED Equation.DSMT4  (x) > 0 ? Over what interval(s) is the graph of F concave up ? If it is known that the graph of F contains the point (a,0), sketch a possible graph of F on the axes below.  Example 3:  The graph of  EMBED Equation.DSMT4 is sketched on the axes above.  EMBED Equation.DSMT4  is continuous on the interval (a,g). Use this graph to answer the following questions. Over what interval(s) is  EMBED Equation.DSMT4  (x)  EMBED Equation.3  0 ? Over what interval(s) is  EMBED Equation.DSMT4  increasing? At what x-values does the graph of F have inflection points ? If  EMBED Equation.DSMT4 (a) = 2, is  EMBED Equation.DSMT4 (c) positive or negative ? Write an argument that supports your conclusion. Example 4: The graphs of H, H ’, and H ’’ are sketched on the axes above and G, G’, and G” are sketched below. Determine which is which, and clearly explain your reasoning.  1989 AB5  Note: This is the graph of the derivative of f, not the graph of f The figure above shows the graph of  EMBED Equation.3 , the derivative of a function  EMBED Equation.3 . The domain of  EMBED Equation.3  is the set of all real numbers x such that -10  EMBED Equation.3  x  EMBED Equation.3  10. For what values of x does the graph of  EMBED Equation.3  have a horizontal tangent? For what values of x in the interval (-10,10) does  EMBED Equation.3  have a relative maximum? Justify your answer. For what values of x is the graph of  EMBED Equation.3  concave downward? 1985 AB6  Note: This is the graph of the derivative of f, not the graph of f The figure above shows the graph of  EMBED Equation.3 , the derivative of a function  EMBED Equation.3 . The domain of the function  EMBED Equation.3  is the set of all x such that - 3  EMBED Equation.3  x  EMBED Equation.3  3. For what values of x, -3 < x < 3, does  EMBED Equation.3  have a relative maximum? A relative minimum? Justify your answer. For what values of x is the graph of  EMBED Equation.3  concave up ? Justify your answer. Use the information found in parts (a) and (b) and the fact that  EMBED Equation.3 ( -3)=0 to sketch a possible graph of  EMBED Equation.3 . The Fundamental Theorem of Integral Calculus What is so fundamental about the Fundamental Theorem? To a mathematician, the "fundamental theorems" are those that are the foundations for the subject being addressed. This is certainly true for the Fundamental Theorem of Arithmetic (which states that every positive integer greater than 1 is either prime or can be written as a product of primes in essentially one way) and the Fundamental Theorem of Algebra (which states that every polynomial equation of degree n EMBED Equation.2  with complex coefficients has at least one root, which is a complex number.) For many years before the Fundamental Theorem of Calculus was proved, mathematicians worked with derivatives, antiderivatives, and sums of products. After Isaac Barrow discovered and proved the Fundamental Theorem of Calculus, both his student, Isaac Newton, and Gottfried Leibnitz developed many of the concepts of calculus that we use and study today. The power of the Fundamental Theorem of Calculus is that it (i) connects the branches of differentiation and integration, and (ii) provides an efficient means of accumulating rates of change. Let’s discuss possible approaches to the development of this theorem in our classrooms that will enable our students to both understand and appreciate this most powerful and fundamental of theorems. The Area Approach This is probably the most frequently seen textbook and classroom development of the theory behind the Fundamental Theorem. Students relate easily to the concept of area, to the idea of getting better approximations to area by increasing the number of rectangles employed, and the instinctive (and visually appealing) sense that using limits will bring us to an "exact area". Unfortunately, this approach can also be misleading. Since area is of positive magnitude, this approach is built upon the given function being positive on the interval described, and thus neglects the implications of a function that may not (always) be positive on the given interval. Also, this approach does not help build the critical relationship between differentiation and integration except by happenstance. The Distance Approach Just as the Area Approach is based upon the accumulation of small pieces of area, the Distance Approach is based upon the accumulation of small distances. The disadvantage of this approach is that it is not as familiar nor as visual for students. The advantage is that is so beautifully shows the integration process as one of accumulating rates of change, and thus gives clear evidence of the relationship between differentiation and integration. It also has the advantage of allowing velocity (function) values to be either positive or negative or both. The student can literally "see" the contrast between total distance traveled and displacement, a concept which has no parallel in the area approach. A Formal Proof Approach A fairly formal proof of the Fundamental Theorem is given in many textbooks, and is presented in many classrooms. Since few students are neither comfortable with the notation used, nor able to appreciate the theoretical development without some concrete work first, to provide the proof as a sole means of having students grasp the Fundamental Theorem is futile. However, in the "Age of Reform" (drumroll, please) are we expected to present the proof as part of our development? Do we feel that it is productive, useful, or desirable to do so whether or not the Reform movement thinks so? Let us summarize our goals: We want students to understand the Fundamental Theorem. We want students to appreciate its power. We want students to see that the Fundamental Theorem explains the relationship between the two major themes of calculus: integration and differentiation. We want students to see the Fundamental Theorem as providing a powerful tool for accumulating rates of change. A QUESTION OF VELOCITY Mark Saintly entered a Walk-a-Thon to help raise money for the local Community Center. He started the walk slowly, but gradually picked up some speed since there was a bonus $100 contribution made by a local business for any walker who completed the 5 mile walk in less than 100 minutes. The table below shows Mark’s speed at various times along the designated route. Time, in minutes, since Mark began the Walk  0 2 4 8 Mark’s speed in miles per minute  0 .03 .04 .06 Let’s assume that Mark never decreased his speed in these first 8 minutes. Use the information in this table to estimate the distance Mark had covered in the first 8 minutes. Provide not only an answer, but an rationale for why you feel this might be a reasonable estimate. Suppose that we had more information about Mark’s speed than was provided in the first table. Below is a more complete table. Time, in minutes, since Mark began the Walk  0  1 2 4 6 8 Mark’s speed in miles per minute  0 .01 .02 .04 .05 .06 With the additional information, revise your estimate of the distance Mark has covered in the first 8 minutes of the Walk-a-Thon. Based upon your estimate from question 2, what was Mark’s average rate for the first 8 minutes? AN AREA PROBLEM WITH AN OOPS A function, f, given by the rule f(x) = 96 - 32x is sketched on the axes below.  Use the CRiemann program to estimate the area of the trapezoidal region enclosed by the graph of this function, the X-axis, the Y-axis, and the vertical line x = 1. Confirm using geometry. Use the CRiemann program to estimate the area of the triangular region enclosed by the graph of this function, the X-axis, and the Y-axis. Confirm using geometry. Find the total area trapped between this function, the X-axis, and the vertical lines x = 0 and x = 2. Explain the discrepancy with your result and the result when the Criemann program is applied to the same interval. AP Examination Questions Relating to the Fundamental Theorem 1987 BC6 Let f be a continuous function with domain x > 0 and let F be the function given by  EMBED Equation.2  for x > 0 . Suppose the F(ab) = F(a) + F(b) for all a>0 and b>0 and that F ' (1) = 3. (a) Find f(1). (b) Prove that  EMBED Equation.2  for every positive constant  EMBED Equation.2 . (c) Use the results from parts (a) and (b) to find f(x). Justify your answer. 1991 BC4 Let  EMBED Equation.2 . (a) Find F ' (x). (b) Find the domain of F. (c) Find  EMBED Equation.2 . (d) Find the length of the curve y = F(x) for 1 EMBED Equation.2 x EMBED Equation.2 2. 1993 AB Multiple Choice #41  EMBED Equation.2  is (a) 0 (b)  EMBED Equation.2  (c)  EMBED Equation.2  (d)  EMBED Equation.2  (e)  EMBED Equation.2  FUNCTIONS DEFINED BY INTEGRALS There are many functions defined by integrals. Perhaps the most “famous” function of this type from the realm of first year calculus is the natural logarithmic function. In the past, many of us have tended to race past the development of functions defined by integrals to get to functions themselves. In a sense, this is like racing to our destination without “stopping to smell (or even see) the roses” along the way. In our haste to get to the skills of finding antiderivatives, to make our students competent with logarithmic and exponential functions, and to apply the students’ skills to applied problems such as volumes, we have missed some important theory and some wonderful explorations. This presentation hopes to revisit familiar topics with some sight-seeing and exploring along the way. In the Teacher’s Guide: AP Calculus, the goals of AP Calculus have been listed and explained in greater detail. On page 9, the fourth goal is presented and explained: Students should understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus. The fourth goal is for students to understand the Fundamental Theorem of Calculus, which they can really do only after the two previous goals have been met. They should understand “both parts” of the theorem. One part validates the use of antiderivatives to evaluate definite integrals, that is,  EMBED Equation.3 , where  EMBED Equation.3  is any antiderivative of  EMBED Equation.3 . The other part involves the differentiation of functions defined by definite integrals, that is,  EMBED Equation.3 . Students for whom integration is introduced from the outset as “the opposite of differentiation” are understandably less than impressed by the profundity of these results. In order to get the most out of our travels, it will be important for students to have a good grip on the foundations: the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change, and an understanding of the Fundamental Theorem of Calculus. Let’s address the “part” of the Fundamental Theorem most critical to this topic: the part that states  EMBED Equation.3 . One of the recent changes in the content of AB Calculus is that those students are expected to deal with topics at the same depth as their BC Calculus counterparts. Thus, they should be able to apply composition of functions to this concept by using the Chain Rule: that is,  EMBED Equation.3  We will look at ways of helping our students understand this concept. SAMPLE PROBLEMS: Example 1: Given function  EMBED Equation.3 such that  EMBED Equation.3 . Describe the graph of  EMBED Equation.3  as completely as possible, giving explanations to support your conclusions. Be sure to include a discussion of the domain of this function, intervals over which it increases or decreases, and its concavity. Example 2: 1995 AB6 The graph of a differentiable function  EMBED Equation.3  on the closed interval [1,7] is shown. Let  EMBED Equation.3 .  Find  EMBED Equation.3  Find  EMBED Equation.3  On what interval or intervals is the graph of  EMBED Equation.3  concave upward. Justify your answer. Find the value of x at which  EMBED Equation.3  has its maximum on the closed interval [1,7]. Justify your answer. Example 3: 1995 BC6 Let  EMBED Equation.3  be a function whose domain is the closed interval [0,5]. The graph of  EMBED Equation.3  is shown below.  Let  EMBED Equation.3  Find the domain of  EMBED Equation.3  Find  EMBED Equation.3  At what x is  EMBED Equation.3  a minimum? Show the analysis that leads to your conclusion. Example 4: If  EMBED Equation.3  , then find  EMBED Equation.3 . If  EMBED Equation.3  , , then find  EMBED Equation.3 . The variables x and y are related by  EMBED Equation.3  Show that  EMBED Equation.3  is proportional to y and find the constant of proportionality. Example 5: [Based on a problem from Calculus Problems for a New Century , pg.110] Let  EMBED Equation.3  where  EMBED Equation.3  is graphed below.  Does  EMBED Equation.3  have any local maxima on (0,10)? If so, state at what x-values they occur and explain your reasoning for choosing these values. Must  EMBED Equation.3  have an absolute maximum value on the interval [0,10]? Explain why or why not. If  EMBED Equation.3  must have an absolute maximum value on [0,10], find the x-value at which it occurs and support your answer with an explanation of your reasoning. Determine any intervals within (0,10) on which  EMBED Equation.3  will be concave up. Justify your answer. Sketch a possible graph of  EMBED Equation.3 . **Suppose that it is known that g is an even function with domain [-10,10]. Determine the intervals over which g must be concave up. Support your answer with work or an explanation that does not rely on the symmetry of the graph alone. Example 6: 1997 AB5  The graph of a function  EMBED Equation  consists of a semicircle and two line segments as shown above. Let  EMBED Equation  be the function given by  EMBED Equation . Find  EMBED Equation . Find all values of  EMBED Equation  on the open interval (-2,5) at which  EMBED Equation  has a relative maximum. Justify your answer. Write an equation for the line tangent to the graph of  EMBED Equation  at x=3. Find the x-coordinate of each point of inflection of the graph of  EMBED Equation  on the open interval (-2,5). Justify your answer. VARIABLE SEPARABLE DIFFERENTIAL EQUATIONS Differential equations are means of describing relationships between rates of change and other values.  EMBED Equation.2  The above are examples of differential equations relating the rate of change  EMBED Equation.2  to x, to y, or to both. They are each also of the type known as variable separable. Differential equations are classified by type (ordinary or partial), by order (that of the highest order derivative that occurs in a differential equation) and by degree (the exponent of the highest power of the highest order derivative.) For example,  EMBED Equation  is an ordinary differential equation of order three and degree two. . ( To solve a differential equation means to find a family of functions that satisfies the particular differential equation. For example, show that any member of the family  EMBED Equation.2  solves the differential equation  EMBED Equation.2  (To solve a differential equation of the form  EMBED Equation.2  requires finding a function F that whose derivative is f . The most general solution of the given differential equation is thereby y = F(x) + C. For example, given  EMBED Equation.2 , the general solution is  EMBED Equation  because cosine is the derivative function for sine. ( To find a particular family member of the general solution set of a differential equation requires having one or more initial conditions. For example, if we know that  EMBED Equation.2  then we know (1)  EMBED Equation  and also that (2)  EMBED Equation.2 . Thus  EMBED Equation  is the unique particular solution for the differential equation under the given initial conditions. (Often, the method of substitution (used implicitly or explicitly) is a necessary integration technique enabling us to solve a differential equation using the Chain Rule. For example,  EMBED Equation.2  is really of the form  EMBED Equation.2  and so its general solution is  EMBED Equation.2  or, better yet  EMBED Equation.2 . Separation of Variables Some differential equations take the form  EMBED Equation.2  where the rate of change depends not only upon x but also upon y. If this differential equation can be written in the form  EMBED Equation.2  then it can be transformed to  EMBED Equation.2  and solved by antidifferentiating both the left-hand member and the right-hand member with respect to x. Looking at the general form of a variable separable differential equation, it appears that one is integrating the left-hand member with respect to y and the right-hand member with respect to x; not so, however. Suppose we can write a differential equation in the form  EMBED Equation.2  then, we can transform this equation to one of the form  EMBED Equation.2 . (1) This leads to  EMBED Equation.2 , which is the "classic" variable separable format. If y is a function of x, say y(x), and if  EMBED Equation  is an antiderivative of  EMBED Equation  and F(y) is an antiderivative of f(y), we can use the Chain Rule to discover that  EMBED Equation.2  If we rewrite equation (1) as  EMBED Equation  (2) then it is clear ??? that the left member is the result of differentiating  EMBED Equation  with respect to  EMBED Equation  and that the right member is the result of differentiating  EMBED Equation  with respect to  EMBED Equation . Thus we integrate (both sides of) equation (2) with respect to  EMBED Equation  to get  EMBED Equation . 1. Growth and Decay Problems Many quantities are found to increase or decrease (grow or decay) over time in direct proportion to the amount of the quantity present. The resulting differential equations is of the form  EMBED Equation.2  A classic example of this type of problem is a "typical" population problem or a typical radioactive decay problem. For example, 1987 BC1 At any time t EMBED Equation.2 0, in days, the rate of growth of a bacteria population is given by y' = ky where k is a constant a y is the number of bacteria present. The initial population is 1000 and the population triples during the first 5 days. (a) Write an expression for y at any time t EMBED Equation.2 0. (b) By what factor will the population have increased in the first 10 days? (c) At what time t, in days, will the population have increased by a factor of 6? Newton's Law of Cooling(or Heating) Another classic example is Newton's Law of Cooling (or Heating) which states that the rate at which an object cools (or warms) is proportional to the difference in temperature between the object and the temperature of the surrounding medium. Newton's Law of Cooling is an enlightening variation on the population problem. (a) Derive an equation which expresses the temperature T of a cooling object at any time t if the temperature of the surrounding medium is Tm (b) Use your results in part (a) to find a solution to the following problem: You have just baked a fresh apple pie and removed it from the oven at a temperature of 450o F. You have left it to cool in a room whose temperature is maintained at a constant 70o F. The ideal temperature for serving hot apple pie is when the pie has cooled to 100o F. If after half an hour the pie has already cooled to 200o F, when is the ideal time to serve to pie? 1993 AB6 Let P(t) represent the number of wolves in a population at time t years, when t EMBED Equation.2 0. The population P(t) is increasing at a rate directly proportional to 800 - P(t), where the constant of proportionality is k. (a) If P(0) = 500, find P(t) in terms of t and k. (b) If P(2) = 700, find k. (c) Find  EMBED Equation.2 . Coasting to a Stop Consider an object in motion, such as a car, coasting to a stop. There are actually many forces at play in such a context, but if the situation is simplified, it might be assumed that the resisting force encountered is proportional to the velocity. [That is, the slower the object moves, the less resistance it encounters.] From physics, it is known that Force = mass X acceleration . It has been determined that for a 50-kg ice skater, the constant of proportionality described above is about –2.5 kg/sec. How long will it take the skater to coast from 7 m/sec to 1 m/sec ? How far will the skater coast before coming to a complete stop? The Salt Brine Problem At time t = 0 minutes a tank contains 4 lbs. Of salt dissolved in 100 gallons of water. Brine containing 2 lbs. Of salt per gallon of water is allowed to enter the tank at the rate of 5 gal./min. The mixed solution is at the same time allowed to drain from the tank at the same rate. How much salt is in the tank after 10 minutes? Logistic Equation Models from Differential Equations A population growing in a confined environment often follows a logistic growth curve because the rate of growth of the population depends not only upon the existing population but also upon the maximum amount of population the confined environment can support. Such functions are interesting to investigate graphically. They come from the solution of a separable differential equation of the form  EMBED Equation.2  1991 BC6 A certain rumor spreads through the community at the rate  EMBED Equation.3 , where  EMBED Equation.3 is the proportion of the population that has heard the rumor at time  EMBED Equation.3 . (a) What proportion has heard the rumor when it is spreading fastest? If at time t = 0, ten percent of the people have heard the rumor, find  EMBED Equation.3  as a function of time  EMBED Equation.3 . (c) At what time  EMBED Equation.3  is the rumor spreading the fastest? Sample Multiple Choice Questions 1993 AB33 If  EMBED Equation.2  and if y = -1 when x = 1 , then when x = 2, y = (a) -2/3 (b) -1/3 (c) 0 (d) 1/3 (e) 2/3 Note: 62% omitted this problem with only 14% making the correct choice of (b). 1993 BC13 If  EMBED Equation.2 , then y could be (a) 3ln(x/3) (b)  EMBED Equation.2  (c)  EMBED Equation.2  (d)  EMBED Equation.2  (e)  EMBED Equation.2  Note: 17% omitted this question. 45% chose the incorrect answer of (b) and 34% chose the correct answer of (c). THE SLIPPERY SLIDES OF SLOPE FIELDS There are programs for graphing calculators and for computers that will draw slope fields for us. Unfortunately, the resulting “pictures” do not always give an accurate sense of the behavior of the function or relation being investigated. This is where the “slippery slide” can occur. The experience we can provide our students with a paper and pencil introduction to slope fields is undoubtedly the most critical component of the topic at this level. That is, our goals (I would suggest) should be to be certain our students understand the information a first-order differential equation provides. to enable our students to have a real “feel” for the family of solutions to differential equations. To help our students focus on the concepts rather than on the technique alone. Pedagogy: Investigating slope fields After reflecting on slope as a rate of change and the locally linear behavior of a function in neighborhoods of points at which the function is differentiable, ask students to discuss the thoughts that come to mind when presented with a particular differential equation. For example, what does the following equation “mean” to them:  EMBED Equation.3  (Note: I would intentionally pick a first order differential equation that they are not likely to be able to solve at the point you are introducing this topic). Gathering thoughts and then using graph paper and pencil to explore slope values at particular points might be the next order of business. After one or more examples, I would turn the class loose on trying to similarly investigate the following:  EMBED Equation.3  From our graphical display, we might try to make conjectures about a particular family that would behave the way the slope field demands, and then check our conjecture by substituting appropriate derivatives into the differential equation. Hopefully such exploration would reinforce what it means to “solve” a differential equation and what a differential equation describes. Perhaps students will more clearly see differential equations not merely as end results of some random differentiation but also, and more importantly, as providers of descriptive information about the behavior of a family of functions. Throughout the year, this topic can be revisited at appropriate moments. For example, once students know that  EMBED Equation.3 , the solution of many of the above differential equations can be revisited. Assessment: Understanding slope fields The following graphs show slope fields in the particular viewing window provided. For each: Propose a family of functions that would solve the differential equation reflected by the slope field. Explain as completely as you can why you have selected this family. Propose a differential equation whose graph would be the slope field shown. Explain as completely as you can what characteristics of the slope field caused you to select this differential equation. (a) [-4.7,4.7] x [-3.1,3.1] (b) [-4.7,4.7] x [-3.1,3.1] (c) [-4.7,4.7] x [-3.1,3.1] (d) [-4.7,4.7] x [-3.1,3.1]   (e) [-4.7,4.7] x [-3.1,3.1] (f) [-4.7,4.7] x [-3.1,3.1]  Content and Pedagogy: Euler’s Method Slope fields are used to see trends in the behavior of solutions to differential equations. Euler’s method is used to find numerical approximations to solutions of these differential equations. That is, if we are given initial conditions that apply to the solution of a particular differential equation, we can begin at that point in the plane and head off in the direction indicated by the slope field. At some well-chosen point, we make a course correction by re-evaluating the direction we should be heading based upon the differential equation and some new location. Theoretically, if the intervals at which we make our course corrections are small enough, we should be able to piece together a rough, but reasonable, solution. As a first example, a class might begin with the differential equation  EMBED Equation.3  and the initial conditions y = 1 when x = 0. From the differential equation, the slope of a line tangent to the solution’s graph has slope 0 + 1 = 1. Thus, the tangent line  EMBED Equation.3  models that solution. We follow along that line until we are ready to make a course correction. Using that model, y = 2 when x = 1. Therefore, at the point (1,2) we might make a change of direction, heading off along a line with slope of 1 + 2 = 3. Thus, the line EMBED Equation.3  becomes our new model. If we move another unit in the x-direction before changing course, we would arrive at the point (2,5). Using the differential equation, the predicted slope would be 2 + 5 = 7. We then build a new model,  EMBED Equation.3  and continue along this new path. What students would hopefully become suspicious about is the fact that we are making course corrects every horizontal unit of 1. This is not exactly a small increment! Someone might suggest a smaller horizontal increment be used to correct our course. The class could explore what happens when  EMBED Equation.3  = 0.5 or even  EMBED Equation.3 = 0.1 Approximating the solution at x = 2 is markedly different for each choice of  EMBED Equation.3 . At this time, it might be helpful to have students verify that the general solution to this differential equation is  EMBED Equation.3  and that the initial conditions allow us to determine the specific family member  EMBED Equation.3 . The class can then use this solution to compare approximations using Euler’s Method with several step sizes for  EMBED Equation.3 . The three graphs below show the actual particular solution compared with models that start with the tangent at (01,) and progress through several course changes over the interval [0,2] based on  EMBED Equation.3 =1 and then  EMBED Equation.3 =0.5.  Solutions to Slope Field graphs:  EMBED Equation.3  PAGE 1 PAGE 1 AP Calculus Summer Institute 2003, jt sutcliffe PAGE 5 PAGE 50 2003 Summer AP Institute jt sutcliffe  EMBED Word.Picture.8   EMBED Word.Picture.8  *+,-.Lc€’“”•A O Q ď đ ä ďŢĐďÁ´§™§ˆ§lWˆ§G9§ˆ§hĹÍh\ć>*OJQJ^JhĹÍh\ć>*CJOJQJ^J(jaz hĹÍh\ćEHä˙OJQJU^J6jaz hĹÍh\ćCJOJQJUV^JmHnHu!jhĹÍh\ćOJQJU^JhĹÍh\ć5OJQJ^JhĹÍh\ćOJQJ^JhĹÍh>&ĄOJQJ^JhĹÍh\ćCJOJQJ^Jh\ćCJ OJQJ^JaJ hŢx%h\ćCJ OJQJ^JaJ h¸hŢx%CJOJQJ^JaJ+,-.€–ń ň @ A P Q î ď ń ň — ˜ ă ä ć ĐĐĐĘČČĂČČČČĘČČČĂČČČČČĂ$a$$@&a$/$d %d &d 'd -D MĆ ˙ćććNĆ˙ OĆ˙ PĆ˙ QĆ˙ gdŢx%üŞüĺüýýýä ĺ ăä÷řůúĐčHI`abcůú^_îáĐᴟĐááĐáyfĐáĐáP=ĐáĐ%jšhĹÍh\ćEHú˙OJQJU^J+jqČĐ> hĹÍh\ćCJOJQJUV^J%jĽhĹÍh\ćEHň˙OJQJU^J+j—ÄĐ> hĹÍh\ćCJOJQJUV^JhĹÍh\ć>*CJOJQJ^J(jÚ‡6 hĹÍh\ćEHć˙OJQJU^J6jÚ‡6 hĹÍh\ćCJOJQJUV^JmHnHu!jhĹÍh\ćOJQJU^JhĹÍh\ćOJQJ^J!j§hĹÍh\ćOJQJU^Jć ĎĐ꯰^_Îäĺ ĄŞŤw×n?@AB_`ýýřřřýýýýýöýýýóýýîîîîčýýâý$@&a$„•`„• & F@&$a$_vwxyşťëě)*ABCDJKPTóÝĘšóŤóšó•‚šóšólYšóIó;hĹÍh\ć>*OJQJ^JhĹÍh\ć6OJQJ]^J%jöhĹÍh\ćEHř˙OJQJU^J+jüÇĐ> hĹÍh\ćCJOJQJUV^J%jő hĹÍh\ćEHč˙OJQJU^J+jŮÇĐ> hĹÍh\ćCJOJQJUV^JhĹÍh\ćH*OJQJ^J!jhĹÍh\ćOJQJU^J%j hĹÍh\ćEHđ˙OJQJU^J+jTČĐ> hĹÍh\ćCJOJQJUV^JhĹÍh\ćOJQJ^JT_`wxyzą˛ÉĘËĚÎä°ąÂĂÄĹŰÜíóâóĚšâóâóŁâó‡óâókXâóâó%jŽhĹÍh\ćEHô˙OJQJU^J6jw469 hĹÍh\ćCJOJQJUV^JmHnHuhĹÍh\ć^J%j%hĹÍh\ćEHú˙OJQJU^J+jŠČĐ> hĹÍh\ćCJOJQJUV^J%jśhĹÍh\ćEHú˙OJQJU^J+j‚ČĐ> hĹÍh\ćCJOJQJUV^J!jhĹÍh\ćOJQJU^JhĹÍh\ćOJQJ^Jíîďđ   23DEFG`arsäŃŔłŔł—„ŔłŔłhUŔłŔł96jż469 hĹÍh\ćCJOJQJUV^JmHnHu%jphĹÍh\ćEHô˙OJQJU^J6jŤ469 hĹÍh\ćCJOJQJUV^JmHnHu%johĹÍh\ćEHň˙OJQJU^J6j™469 hĹÍh\ćCJOJQJUV^JmHnHuhĹÍh\ćOJQJ^J!jhĹÍh\ćOJQJU^J%jnhĹÍh\ćEHô˙OJQJU^J6j‡469 hĹÍh\ćCJOJQJUV^JmHnHustu—˜ŠŞŤŹŔÁŇÓÔŐ× !ěŰÎŰβŸŰÎŰ΃pŰÎbOb29jŤ469 hĹÍh\ć5CJOJQJUV^JmHnHu$jhĹÍh\ć5OJQJU^JhĹÍh\ć5OJQJ^J%j$hĹÍh\ćEHü˙OJQJU^J6jň469 hĹÍh\ćCJOJQJUV^JmHnHu%j]"hĹÍh\ćEHô˙OJQJU^J6jŤ469 hĹÍh\ćCJOJQJUV^JmHnHuhĹÍh\ćOJQJ^J!jhĹÍh\ćOJQJU^J%j0 hĹÍh\ćEHŕ˙OJQJU^J!"#'(9:;<WXijklnst…ëŘĘŘĘ­˜ŘĘŘĘ{fŘĘYHY!jhĹÍh\ćOJQJU^JhĹÍh\ćOJQJ^J(jľ)hĹÍh\ć5EHň˙OJQJU^J9j"569 hĹÍh\ć5CJOJQJUV^JmHnHu(jÉ'hĹÍh\ć5EHü˙OJQJU^J9j569 hĹÍh\ć5CJOJQJUV^JmHnHuhĹÍh\ć5OJQJ^J$jhĹÍh\ć5OJQJU^J(j &hĹÍh\ć5EHô˙OJQJU^J…†‡ˆ¸šĘËĚÍéęűüýţ():;äŃŔłŔł—„ŔłŔłhUŔłŔł96j"569 hĹÍh\ćCJOJQJUV^JmHnHu%j0hĹÍh\ćEHô˙OJQJU^J6j‡469 hĹÍh\ćCJOJQJUV^JmHnHu%jŽ-hĹÍh\ćEHŕ˙OJQJU^J6jŸ569 hĹÍh\ćCJOJQJUV^JmHnHuhĹÍh\ćOJQJ^J!jhĹÍh\ćOJQJU^J%jź+hĹÍh\ćEHň˙OJQJU^J6j3569 hĹÍh\ćCJOJQJUV^JmHnHu;<=B^Ž!Ę!Ü!Ý!é!ę!ě!"""""" 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EFEquation.DSMT4ô9˛qeÝ@6Mů6GĚëxDSMT4WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/APôG_APňAPôAôEô%ôB_AôC_Aň Ľň %ô!ôAôHôôAň_D_Eô_Eô_A  ƒfƒx–(CompObj˙˙˙˙1iObjInfo˙˙˙˙˙˙˙˙3Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙4$_1053870193˙˙˙˙˙˙˙˙ÎŔFe$@’˜Ăe$@’˜Ă–)†==ƒx ˆ2ţ˙ ˙˙˙˙ÎŔFMathType 4.0 Equation MathType EFEquation.DSMT4ô9˛qeÝÔ@6Mů6GĚëxDSMT4WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/APôG_APňAPôAôEô%ôB_AôC_Aň Ľň %ô!ôAôHôôAňOle ˙˙˙˙˙˙˙˙˙˙˙˙9CompObj˙˙˙˙:iObjInfo˙˙˙˙˙˙˙˙<Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙=đ_D_Eô_Eô_A  ƒaţ˙ ˙˙˙˙ÎŔFMathType 4.0 Equation MathType EFEquation.DSMT4ô9˛qeÝ@6Mů6GĚëxDSMT4WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/APôG_APňAPôAôEô%ôB_AôC_Aň Ľň %ô!ôAôHôôAň_1053870164&ÎŔFe$@’˜Ăe$@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ACompObj˙˙˙˙BiObjInfo˙˙˙˙ ˙˙˙˙DEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙E _1053870041,+#ÎŔFe$@’˜Ă ë%@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙JCompObj"$˙˙˙˙Ki_D_Eô_Eô_A  ƒa‚,ƒa ˆ2 –(–)ţ˙ ˙˙˙˙ÎŔFMathType 4.0 Equation MathType EFEquation.DSMT4ô9˛qeÝ @6Mů6GĚëxDSMT4WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/EObjInfo˙˙˙˙%˙˙˙˙MEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙N<_1053870076˙˙˙˙˙˙˙˙(ÎŔF ë%@’˜Ă ë%@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙SD/APôG_APňAPôAôEô%ôB_AôC_Aň Ľň %ô!ôAôHôôAň_D_Eô_Eô_A   ƒx ˆ2 †"-ƒa ˆ2 ƒx†"-ƒaţ˙ ˙˙˙˙ÎŔFMathType 4.0 Equation MathType EFEquation.DSMT4ô9˛qeÝô@6Mů6GĚëxDSMT4WinAllBasicCodePagesCompObj')˙˙˙˙TiObjInfo˙˙˙˙*˙˙˙˙VEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙W_1053870210ˇ-ÎŔF ë%@’˜Ă ë%@’˜ĂArialSymbolCourier NewTimes New RomanMT Extra!/ED/APôG_APňAPôAôEô%ôB_AôC_Aň Ľň %ô!ôAôHôôAň_D_Eô_Eô_A  ƒx†++ƒa‚,ƒx†`"šƒaţ˙ ˙˙˙˙ÎŔFMathType 4.0 Equation MathType EFEquation.DSMT4ô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙\CompObj,.˙˙˙˙]iObjInfo˙˙˙˙/˙˙˙˙_Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙`đeÝÔ@6Mů6GĚëxDSMT4WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/APôG_APňAPôAôEô%ôB_AôC_Aň Ľň %ô!ôAôHôôAň_D_Eô_Eô_A  ƒaţ˙ ˙˙˙˙ÎŔFMathType 4.0 Equation MathType EFEquation.DSMT4ô9˛q_1053870249˙˙˙˙˙˙˙˙2ÎŔF ë%@’˜Ă ë%@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙dCompObj13˙˙˙˙eiObjInfo˙˙˙˙4˙˙˙˙gEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙hô_959853687…:7 ŔF ë%@’˜Ă ë%@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙lCompObj68˙˙˙˙m\eÝŘ@6Mů6GĚëxDSMT4WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/APôG_APňAPôAôEô%ôB_AôC_Aň Ľň %ô!ôAôHôôAň_D_Eô_Eô_A  ˆ2ƒaţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€ObjInfo˙˙˙˙9˙˙˙˙oOle10Native˙˙˙˙˙˙˙˙˙˙˙˙pD_959853703˙˙˙˙˙˙˙˙< ŔF ë%@’˜Ă ë%@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙r@ ƒfppđŕŕţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒf‚(ˆ1‚)†=ˆ4CompObj;=˙˙˙˙s\ObjInfo˙˙˙˙>˙˙˙˙uOle10Native˙˙˙˙˙˙˙˙˙˙˙˙vD_959853721gSA ŔF ë%@’˜Ă ë%@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙xCompObj@B˙˙˙˙y\ObjInfo˙˙˙˙C˙˙˙˙{Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙|Dţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒx‚,ƒy–(–)ţ˙ ˙˙˙˙ ŔFMathType Equation Equation _959853739˙˙˙˙˙˙˙˙F ŔF ë%@’˜Ă ë%@’˜ĂOle 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Extra!/ECompObjÇÉ˙˙˙˙;iObjInfo˙˙˙˙Ę˙˙˙˙=Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙>L_1097937793!ýÍÎŔFŕř(@’˜Ăŕř(@’˜ĂD/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx ˆ1 –(–)†<<ƒfƒx ˆ2 –(–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙DCompObjĚÎ˙˙˙˙EiObjInfo˙˙˙˙Ď˙˙˙˙GEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙H€ŕřˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx–(–)†>>ˆ0ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q_1097937811˙˙˙˙ŐŇÎŔFŕř(@’˜Ăŕř(@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙MCompObjŃÓ˙˙˙˙NiObjInfo˙˙˙˙Ô˙˙˙˙P€ŕ܈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒx†"΃Iţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙Qř_1097937827˙˙˙˙˙˙˙˙×ÎŔF€*@’˜Ă€*@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙UCompObjÖŘ˙˙˙˙ViObjInfo˙˙˙˙Ů˙˙˙˙XEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙Yđ_1097999046˙˙˙˙˙˙˙˙ÜÎŔFŕř(@’˜Ăŕř(@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙]€ŕԈězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qCompObjŰÝ˙˙˙˙^iObjInfo˙˙˙˙Ţ˙˙˙˙`Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙a_1097999067ńáÎŔFŕř(@’˜Ăŕř(@’˜ĂÝüˆěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  @ƒfƒx–(–)†>>ˆ0ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathTyOle ˙˙˙˙˙˙˙˙˙˙˙˙fCompObjŕâ˙˙˙˙giObjInfo˙˙˙˙ă˙˙˙˙iEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙jđpe EFEquation.DSMT4ô9˛qÝԈěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  @ƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathTy_1097999079˙˙˙˙˙˙˙˙ćÎŔFŕř(@’˜Ăŕř(@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙nCompObjĺç˙˙˙˙oiObjInfo˙˙˙˙č˙˙˙˙qpe 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˙˙˙˙˙˙˙˙˙˙˙˙Ÿ$_1097938601˙˙˙˙ÎŔF€*@’˜Ă€*@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙¤ArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx–(–)†==ƒx ˆ3ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qCompObj˙˙˙˙ĽiObjInfo˙˙˙˙˙˙˙˙§Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙¨đ_1097938611˙˙˙˙˙˙˙˙ ÎŔF`/@’˜Ă`/@’˜Ă€ŕԈězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfďďďţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙ŹCompObj ˙˙˙˙­iObjInfo˙˙˙˙ ˙˙˙˙ŻEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙°€ŕřˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  †"-†"Ľ‚,†"Ľ–(–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q_1097938635ÎŔF€*@’˜Ă€*@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ľCompObj ˙˙˙˙śiObjInfo˙˙˙˙˙˙˙˙¸€ŕřˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT 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Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ˆ0‚,†"Ľ–(–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q€ŕԈězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_1097938800%9"ÎŔF€*@’˜Ă€*@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ŮCompObj!#˙˙˙˙ÚiObjInfo˙˙˙˙$˙˙˙˙ÜEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ýđ_1097938799˙˙˙˙˙˙˙˙'ÎŔF€*@’˜Ă€*@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙áCompObj&(˙˙˙˙âi_D_Eô_Eô_A  ƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q€ŕԈězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*ObjInfo˙˙˙˙)˙˙˙˙äEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙ĺđ_1097999102ä/,ÎŔF€*@’˜Ă€*@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙é_D_Eô_Eô_A  ƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝřˆěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*CompObj+-˙˙˙˙ęiObjInfo˙˙˙˙.˙˙˙˙ěEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙í_1097999115˙˙˙˙˙˙˙˙1ÎŔF€*@’˜Ă€*@’˜Ă_D_Eô_Eô_A  @†"-†"Ľ‚,ˆ0–(–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝԈěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/EOle ˙˙˙˙˙˙˙˙˙˙˙˙ňCompObj02˙˙˙˙óiObjInfo˙˙˙˙3˙˙˙˙őEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙öđD/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  @‹*"Uţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝôˆěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/E_1097999128*y6ÎŔF€*@’˜Ă€*@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙úCompObj57˙˙˙˙űiObjInfo˙˙˙˙8˙˙˙˙ýEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙ţ_1097939161˙˙˙˙˙˙˙˙=  ŔF€*@’˜Ă€*@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙Text :<˙˙˙˙€*@’˜Ă€*@’˜Ăţ˙˙˙ţ˙˙˙     ţ˙˙˙ !"#$ţ˙˙˙&ţ˙˙˙ţ˙˙˙)*+,-ţ˙˙˙ţ˙˙˙0ţ˙˙˙ţ˙˙˙345ţ˙˙˙ţ˙˙˙8ţ˙˙˙ţ˙˙˙;<=>ţ˙˙˙ţ˙˙˙Aţ˙˙˙ţ˙˙˙DEFGţ˙˙˙ţ˙˙˙Jţ˙˙˙ţ˙˙˙MNOPţ˙˙˙ţ˙˙˙Sţ˙˙˙ţ˙˙˙VWXţ˙˙˙ţ˙˙˙[ţ˙˙˙ţ˙˙˙^_`aţ˙˙˙ţ˙˙˙dţ˙˙˙ţ˙˙˙ghiţ˙˙˙ţ˙˙˙lţ˙˙˙ţ˙˙˙opqrţ˙˙˙ţ˙˙˙uţ˙˙˙ţ˙˙˙xyz{ţ˙˙˙ţ˙˙˙~ţ˙˙˙ţ˙˙˙D/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  @ˆ0‚,†"Ľ–(–)[ 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5.0 Equation MathTyOle ˙˙˙˙˙˙˙˙˙˙˙˙6CompObjHJ˙˙˙˙7iObjInfo˙˙˙˙K˙˙˙˙9Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙: pe EFEquation.DSMT4ô9˛q€ŕđˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ˆ1‚,ˆ3–[–]ţ_1097939439GQNÎŔF ,@’˜Ă ,@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙?CompObjMO˙˙˙˙@iObjInfo˙˙˙˙P˙˙˙˙Bţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q€ŕđˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfˆ2–(–)Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙C _1097939495˙˙˙˙VSÎŔF ,@’˜Ă ,@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙HCompObjRT˙˙˙˙Iiý˙˙˙ƒ„…†‡ˆŠ‰‹ŒŽ‘’ô“”–•—˜™š›œŢߟ Ą˘Ł¤ĽŚ§¨ŠŞŤŹ­ŽŻ°ą˛ł´ľśˇ¸šşťź˝žżŔÁÂĂÄĹĆÇČÉĘËĚÍÎĎĐŃŇÓÔŐÖ×ŘŮÚŰÜÝ,áŕâăäĺćçčéęëěíîđďńňóőö÷řůúűüţý˙ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q€ŕˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  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,@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙jCompObjfh˙˙˙˙kiD/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfďďďţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q€ŕđˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/EObjInfo˙˙˙˙i˙˙˙˙mEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙n _1097999160˙˙˙˙˙˙˙˙lÎŔF ,@’˜Ă ,@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙sD/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A   ˆ0‚,†"Ľ–[–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝřˆěz.h`ězDSMT5WinAllBasicCodePagesCompObjkm˙˙˙˙tiObjInfo˙˙˙˙n˙˙˙˙vEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙w_1097999178jtqÎŔF ,@’˜Ă ,@’˜ĂArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  @†"-†"Ľ‚,ˆ0–(–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙|CompObjpr˙˙˙˙}iObjInfo˙˙˙˙s˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙€‚ƒ„ţ˙˙˙ţ˙˙˙‡ţ˙˙˙ţ˙˙˙Š‹Œţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙’“”ţ˙˙˙ţ˙˙˙—ţ˙˙˙ţ˙˙˙š›œţ˙˙˙ţ˙˙˙Ÿţ˙˙˙ţ˙˙˙˘Ł¤Ľţ˙˙˙ţ˙˙˙¨ţ˙˙˙ţ˙˙˙ŤŹ­ţ˙˙˙ţ˙˙˙°ţ˙˙˙ţ˙˙˙ł´ľśţ˙˙˙ţ˙˙˙šţ˙˙˙ţ˙˙˙ź˝žţ˙˙˙ţ˙˙˙Áţ˙˙˙ţ˙˙˙ÄĹĆţ˙˙˙ţ˙˙˙Éţ˙˙˙ţ˙˙˙ĚÍÎĎţ˙˙˙ţ˙˙˙Ňţ˙˙˙ţ˙˙˙ŐÖ×Řţ˙˙˙ţ˙˙˙Űţ˙˙˙ţ˙˙˙Ţßŕţ˙˙˙ţ˙˙˙ăţ˙˙˙ţ˙˙˙ćçčéţ˙˙˙ţ˙˙˙ěţ˙˙˙ţ˙˙˙ďđńňţ˙˙˙ţ˙˙˙őţ˙˙˙ţ˙˙˙řůúűţ˙˙˙ţ˙˙˙ţţ˙˙˙ţ˙˙˙Ýôˆěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  @ˆ0‚,†"Ľ–(–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q_1097999192˙˙˙˙˙˙˙˙vÎŔF ,@’˜Ă ,@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙…CompObjuw˙˙˙˙†iObjInfo˙˙˙˙x˙˙˙˙ˆÝԈěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  @ƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙‰đ_1097999210oƒ{ÎŔF ,@’˜Ă ,@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjz|˙˙˙˙ŽiObjInfo˙˙˙˙}˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙‘ü_1097999228˙˙˙˙˙˙˙˙€ÎŔF ,@’˜Ă ,@’˜ĂOle 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Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒx†"΃a‚ObjInfo˙˙˙˙Ľ˙˙˙˙ÓEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ô_1097984129˙˙˙˙˙˙˙˙¨ÎŔFŔŒ-@’˜ĂŔŒ-@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙Ů,ƒb–(–)Ă ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝԈězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*CompObj§Š˙˙˙˙ÚiObjInfo˙˙˙˙Ş˙˙˙˙ÜEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ýđ_1097984141œ°­ÎŔFŔŒ-@’˜ĂŔŒ-@’˜Ă_D_Eô_Eô_A  ƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝđˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*Ole ˙˙˙˙˙˙˙˙˙˙˙˙áCompObjŹŽ˙˙˙˙âiObjInfo˙˙˙˙Ż˙˙˙˙äEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙ĺ _D_Eô_Eô_A  ƒa‚,ƒb–(–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝřˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/E_1097984163˙˙˙˙ľ˛ÎŔFŔŒ-@’˜ĂŔŒ-@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ęCompObjął˙˙˙˙ëiObjInfo˙˙˙˙´˙˙˙˙íEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙î_1097984195˙˙˙˙˙˙˙˙ˇÎŔFŔŒ-@’˜ĂŔŒ-@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙óCompObjś¸˙˙˙˙ôiD/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒc–(–)†==ˆ0ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝřˆězh`ězDSMT5WinAllBasicCodePagesObjInfo˙˙˙˙š˙˙˙˙öEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙÷_1097984216ŤŘźÎŔFŔŒ-@’˜ĂŔŒ-@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙üArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒc–(–)†>>ˆ0ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qCompObjť˝˙˙˙˙ýiObjInfo˙˙˙˙ž˙˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ř_1097999372˙˙˙˙ÎÁÎŔFŔŒ-@’˜ĂŔŒ-@’˜Ăţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙    ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙#$%&ţ˙˙˙ţ˙˙˙)ţ˙˙˙ţ˙˙˙,-./ţ˙˙˙ţ˙˙˙2ţ˙˙˙ţ˙˙˙567ţ˙˙˙ţ˙˙˙:ţ˙˙˙ţ˙˙˙=>?@ţ˙˙˙ţ˙˙˙Cţ˙˙˙ţ˙˙˙FGHIţ˙˙˙ţ˙˙˙Lţ˙˙˙ţ˙˙˙OPQRţ˙˙˙ţ˙˙˙Uţ˙˙˙ţ˙˙˙XYZţ˙˙˙ţ˙˙˙]ţ˙˙˙ţ˙˙˙`abcţ˙˙˙ţ˙˙˙fţ˙˙˙ţ˙˙˙ijkţ˙˙˙ţ˙˙˙nţ˙˙˙ţ˙˙˙qrsţ˙˙˙ţ˙˙˙vţ˙˙˙ţ˙˙˙yz{ţ˙˙˙ţ˙˙˙~ţ˙˙˙ţ˙˙˙Ý܈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒx†==ƒcţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjŔÂ˙˙˙˙iObjInfo˙˙˙˙Ă˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ýüˆěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  @ƒfƒx–(–)†>>ˆ0ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q_1097984671˙˙˙˙˙˙˙˙ĆÎŔFš0@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ CompObjĹÇ˙˙˙˙iObjInfo˙˙˙˙Č˙˙˙˙݈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx–(–)†==ƒx ˆ4ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathTyEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙$_1097984691Ä˙˙˙˙ËÎŔF`/@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjĘĚ˙˙˙˙ipe EFEquation.DSMT4ô9˛qÝԈězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathTyObjInfo˙˙˙˙Í˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙đ_1098001724˙˙˙˙˙˙˙˙ĐÎŔF`/@’˜Ă`/@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjĎŃ˙˙˙˙iObjInfo˙˙˙˙Ň˙˙˙˙!Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙"_1097984770É˙˙˙˙ŐÎŔF`/@’˜Ă`/@’˜Ăpe EFEquation.DSMT4ô9˛q݈ěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A   @ƒf  @ˆ0–(–)†==ˆ0Ole ˙˙˙˙˙˙˙˙˙˙˙˙'CompObjÔÖ˙˙˙˙(iObjInfo˙˙˙˙×˙˙˙˙*Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙+,ý˙˙˙     | !#"$%'&()+*lm-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijkľnopqrtsuvwxyz{}~Ľƒţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q݈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx–(–)†==ˆ4ƒx ˆ3_1097984831ÓâÚÎŔF`/@’˜Ă`/@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙0CompObjŮŰ˙˙˙˙1iObjInfo˙˙˙˙Ü˙˙˙˙3ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝ؈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙4ô_1097984865˙˙˙˙˙˙˙˙ßÎŔF`/@’˜Ă`/@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙8CompObjŢŕ˙˙˙˙9iţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q݈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx–(–ObjInfo˙˙˙˙á˙˙˙˙;Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙<$_1097984921ÝçäÎŔF`/@’˜Ă`/@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙A)†==ƒx ˆ3ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝđˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*CompObjăĺ˙˙˙˙BiObjInfo˙˙˙˙ć˙˙˙˙DEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙E _1097984936˙˙˙˙ěéÎŔF`/@’˜Ă`/@’˜Ă_D_Eô_Eô_A  ˆ0‚,†"Ľ–(–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝřˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/EOle ˙˙˙˙˙˙˙˙˙˙˙˙JCompObjčę˙˙˙˙KiObjInfo˙˙˙˙ë˙˙˙˙MEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙ND/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  †"-†"Ľ‚,ˆ0–(–)ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝ܈ězh`ězDSMT5WinAllBasicCodePages_1097984971˙˙˙˙˙˙˙˙îÎŔFš0@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙SCompObjíď˙˙˙˙TiObjInfo˙˙˙˙đ˙˙˙˙VEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙Wř_1097985012şóÎŔF`/@’˜Ă`/@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙[CompObjňô˙˙˙˙\iArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒx†==ˆ0ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q݈ězh`ězDSMT5WinAllBasicCodePagesObjInfo˙˙˙˙ő˙˙˙˙^Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙_8_1097985458űřÎŔFš0@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙dArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx–(–)†==†"-ƒx  ˆ2ˆ3ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qCompObj÷ů˙˙˙˙eiObjInfo˙˙˙˙ú˙˙˙˙gEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙hđ_1097985431˙˙˙˙ýÎŔFš0@’˜Ăš0@’˜ĂÝԈězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  Ŕƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙lCompObjüţ˙˙˙˙miObjInfo˙˙˙˙˙˙˙˙˙oEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙pôÝ؈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  Ŕƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q_1097985471˙˙˙˙˙˙˙˙ÎŔFš0@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙tCompObj˙˙˙˙uiObjInfo˙˙˙˙˙˙˙˙wEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙xđ_1097985448˙˙˙˙˙˙˙˙ÎŔFš0@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙|CompObj˙˙˙˙}iÝԈězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  Ŕƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qObjInfo˙˙˙˙ ˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙€ô_1097985719ö ÎŔFš0@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙„‚ƒţ˙˙˙ţ˙˙˙†ţ˙˙˙ţ˙˙˙‰Š‹Œţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙’“”ţ˙˙˙ţ˙˙˙—ţ˙˙˙ţ˙˙˙š›œţ˙˙˙ţ˙˙˙Ÿţ˙˙˙ţ˙˙˙˘Ł¤ţ˙˙˙ţ˙˙˙§ţ˙˙˙ţ˙˙˙ŞŤŹ­ŽŻ°ąţ˙˙˙ţ˙˙˙´ţ˙˙˙ţ˙˙˙ˇ¸šşţ˙˙˙ţ˙˙˙˝ţ˙˙˙ţ˙˙˙ŔÁÂţ˙˙˙ţ˙˙˙Ĺţ˙˙˙ţ˙˙˙ČÉĘËţ˙˙˙ţ˙˙˙Îţ˙˙˙ţ˙˙˙ŃŇÓţ˙˙˙ţ˙˙˙Öţ˙˙˙ţ˙˙˙ŮÚŰţ˙˙˙ţ˙˙˙Ţţ˙˙˙ţ˙˙˙áâăţ˙˙˙ţ˙˙˙ćţ˙˙˙ţ˙˙˙éęëěţ˙˙˙ţ˙˙˙ďţ˙˙˙ţ˙˙˙ňóôţ˙˙˙ţ˙˙˙÷ţ˙˙˙ţ˙˙˙úűüýţ˙˙˙ţ˙˙˙Ý؈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  Ŕƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qCompObj  ˙˙˙˙…iObjInfo˙˙˙˙˙˙˙˙‡Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ˆ4_1097985785˙˙˙˙˙˙˙˙ÎŔFš0@’˜Ăš0@’˜Ă݈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx–(–)†==ƒx  ˆ1ˆ3ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj˙˙˙˙ŽiObjInfo˙˙˙˙˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙‘ôÝ؈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛q_1097985802ÎŔFš0@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙•CompObj˙˙˙˙–iObjInfo˙˙˙˙˙˙˙˙˜Ý܈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒx†==ˆ0ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙™ř_1097985842˙˙˙˙˙˙˙˙ÎŔFš0@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj˙˙˙˙žiObjInfo˙˙˙˙˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ąř_1097985952 < ÎŔFš0@’˜Ăš0@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ĽÝ܈ězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒx†==ˆ0ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qCompObj!˙˙˙˙ŚiObjInfo˙˙˙˙"˙˙˙˙¨Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Š _1097986176˙˙˙˙˙˙˙˙%ÎŔFš0@’˜Ăš0@’˜ĂÝđˆězh`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx–(–)†==ƒx†"-ˆ1–(–) ˆ2 †++ˆ2, for ƒx†d"Łˆ2†"-ƒx†"-ˆ1–(–) ˆ2 †++ˆ4, for ƒx†>>ˆ2–{ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝřˆěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/EOle ˙˙˙˙˙˙˙˙˙˙˙˙˛CompObj$&˙˙˙˙łiObjInfo˙˙˙˙'˙˙˙˙ľEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙śD/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfˆ0–(–)†==ˆ0ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝ؈ěz.h`ězDSMT5WinAllBasicCodePages_1097986322#2*ÎŔFš0@’˜Ă  2@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ťCompObj)+˙˙˙˙źiObjInfo˙˙˙˙,˙˙˙˙žEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙żô_1097987080˙˙˙˙˙˙˙˙/ÎŔF  2@’˜Ă  2@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ĂCompObj.0˙˙˙˙ÄiArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝđˆěz.h`ězDSMT5WinAllBasicCodePages`!đŤzŽ“™MœE?}P˘ôßAô  Č˝„yţxÚEQÍJĂ@žÝ4j ­Őƒ =Ú˘ŕÝmě%Rl‹Ç5Ő@ŇHў|€ř>ˆŔ‹ ř"{ŒłŰ Ë.óÍěü}3ŠJPH@œ>J¨( ͲLZZdEZv(şJTŚŁ }":Š#ڞÓ`2TŃň‚řßbCËšW,'šNŻ\]f)Š|T %zBZ2ú›Ţ˙ČŚŕ‘ˆşŘ¤Î"ĎńŃUŘ?ě–ħđ#›$ŻńţWc4zUPęŹáúą7ažßqbďĚĎÝžsáĆPSgškĘ`œ†T#źŽ<7ŇÝԆ^ŕĆëGaŕL V°†şy›D,ÂÂFŰLťmxU;°Y˙k}őů˛Ć€›|‹§›‰/CˆÔä ťÇSiŮGy×CŔv×6š¸LŤäC($M˝‚{Ŕé”ęcÁ÷–bâd6¨|nU˜—ÚłÜćŮLăÄ fűmb>!?1H‘~żŕĺf#ČDd X88đJ˛ đ° C đA?ż ˙"ńż€đ?€2đ*ŹiŽ†w8ď„Es7 ŒţĽ˙ř™`!đţŹiŽ†w8ď„Es7 ŒţĽ Ŕ€ĐĎhßĚţxڍRĎKAţŢŹŠ5’¨=EcÁbƒ?¨ŕ˝k˛(B$˜HË¤.şIRڜ –öOž=÷o(%˙‹wٓÚĆ÷f×(ęÁٝoŢžůć˝ď=Â`ý$@á2†x*"Äx%Őď÷e‘&ĺŁbWƒF"”Pճƽ•Ä[ôĺ HąĽÇř7ώdůÄhä•@AˇöĘí80,#§M¨ż´hN_Ť›g&ŞcšVń“*ľk•z$Q-°•ăÇr\|Äe.ŠI8nÔË8Čdxń„ëÀë”~QČŐů{.aËŘ _W}OČE¸ćYĺ;ŽsŃł\÷qĹ\"’ŽlŹŁHÉŤ’ŰŰçˆIáňĽBy4ţŮߡŤŐUÝôżäę;^QďzM¤cá-i+R!ËŐż6|Ż‘ŮôžńŽěןŚŕĚV˝Ś÷‘*”3Î÷VCc Żg–œn~)‡ •\síâĺô”] Ţ$mN0tW][~ĺdé:AÖ]şĆň‰×ĂuvÖÍťN ŻLŤCŠgFœąĹ9łNqAÄ/›héÍyAŕdN>RœÝ$=–‘ş) ›ÝÓ§|ÇťRťŮňja…VĘ2~ˇüYˆ#uDd 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ţ˙˙˙ţ˙˙˙  ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙!ţ˙˙˙ţ˙˙˙$%&'(ţ˙˙˙ţ˙˙˙+ţ˙˙˙ţ˙˙˙.ţ˙˙˙ţ˙˙˙1ţ˙˙˙ţ˙˙˙4ţ˙˙˙ţ˙˙˙7ţ˙˙˙ţ˙˙˙:ţ˙˙˙ţ˙˙˙=ţ˙˙˙ţ˙˙˙@ţ˙˙˙ţ˙˙˙Cţ˙˙˙ţ˙˙˙FGţ˙˙˙ţ˙˙˙Jţ˙˙˙ţ˙˙˙MNţ˙˙˙ţ˙˙˙Qţ˙˙˙ţ˙˙˙Tţ˙˙˙ţ˙˙˙Wţ˙˙˙ţ˙˙˙Zţ˙˙˙ţ˙˙˙]ţ˙˙˙ţ˙˙˙`ţ˙˙˙ţ˙˙˙cţ˙˙˙ţ˙˙˙fgţ˙˙˙ţ˙˙˙jţ˙˙˙ţ˙˙˙mnţ˙˙˙ţ˙˙˙qţ˙˙˙ţ˙˙˙tuţ˙˙˙ţ˙˙˙xţ˙˙˙ţ˙˙˙{|ţ˙˙˙ţ˙˙˙ţ˙˙˙pe EFEquation.DSMT4ô9˛qÝđˆěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfƒx–(–)Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ _1097988098PZWÎŔFPÎ3@’˜ĂPÎ3@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjVX˙˙˙˙iţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝ؈ěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfý˙˙˙‚„…†‡ˆ‰ŠŒ‹Ž‘’“”–•—˜™›šœžŸ Ą˘ŁŚ¤§ ¨ŠŤŞŹŽ­Ż°ą˛ł´őöśˇ¸šşťź˝žżŔÁÂĂÄĹĆÇČÉĘËĚÍÎĎĐŃŇÓÔŐÖ×ŘŮÚŰÜÝŢßŕáâăäĺćçčéęëěíîďđńňóôo÷ůřűúýüţ˙ObjInfo˙˙˙˙Y˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ ô_1097988127˙˙˙˙˙˙˙˙\ÎŔFPÎ3@’˜ĂPÎ3@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj[]˙˙˙˙iObjInfo˙˙˙˙^˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙đ_1097993586˙˙˙˙˙˙˙˙aÎŔFPÎ3@’˜ĂPÎ3@’˜Ăţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝԈěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒfOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj`b˙˙˙˙iObjInfo˙˙˙˙c˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ôţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝ؈ěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒf_1097993672_ÚfÎŔFPÎ3@’˜ĂPÎ3@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjeg˙˙˙˙ iObjInfo˙˙˙˙h˙˙˙˙"ţ˙ ˙˙˙˙ÎŔFMathType 5.0 Equation MathType EFEquation.DSMT4ô9˛qÝ,ˆěz.h`ězDSMT5WinAllBasicCodePagesArialSymbolCourier NewTimes New RomanMT Extra!/ED/CôG_APňAPôAôEô%ôB_AôC_AôEô*_HôAô@ôAHôA*_D_Eô_Eô_A  ƒx ƒo ‚,ƒfƒx ƒo –(–)–(Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙#H_990363704Ě}k ŔFPÎ3@’˜ĂPÎ3@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙)CompObjjl˙˙˙˙*\–)ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒx†=ƒaV Ŕw ObjInfo˙˙˙˙m˙˙˙˙,Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙-D_990363685˙˙˙˙˙˙˙˙p ŔFŰ6@’˜ĂŰ6@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙/CompObjoq˙˙˙˙0\ObjInfo˙˙˙˙r˙˙˙˙2Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙3D_990363660nu ŔFŰ6@’˜ĂŰ6@’˜Ăţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒgîYHV Ŕw ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙5CompObjtv˙˙˙˙6\ObjInfo˙˙˙˙w˙˙˙˙8Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙9D€@ ƒhXPV Ŕw ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒx†=ƒaV Ŕw _990363738˙˙˙˙˙˙˙˙z ŔFŰ6@’˜ĂŰ6@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙;CompObjy{˙˙˙˙<\ObjInfo˙˙˙˙|˙˙˙˙>Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙?D_990363755x‚ ŔFđT5@’˜ĂđT5@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ACompObj~€˙˙˙˙B\ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€ˆ ƒfƒx–(–)†=ƒgƒx–(–)†+ƒhƒx–(–)hJs;fKt<eKu<Żĺ˙˙D˙D˙ObjInfo˙˙˙˙˙˙˙˙DOle10Native˙˙˙˙˙˙˙˙˙˙˙˙EŒ_990363843˙˙˙˙˙˙˙˙„ ŔFđT5@’˜ĂđT5@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙Hţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ 2ƒfƒa–(–)†=2ƒgƒa–(–)†+2ƒhƒa–(–)"Embedded ObjecCompObjƒ…˙˙˙˙I\ObjInfo˙˙˙˙†˙˙˙˙KOle10Native˙˙˙˙˙˙˙˙˙˙˙˙L„_990364152i‘‰ ŔFđT5@’˜ĂđT5@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙OCompObjˆŠ˙˙˙˙P\ObjInfo˙˙˙˙‹˙˙˙˙ROle10Native˙˙˙˙˙˙˙˙˙˙˙˙Sdţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒfƒx–(–)†=ƒk†×ƒgƒx–(–)Ŕ´DI3Sţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q_990364174˙˙˙˙˙˙˙˙Ž ŔFđT5@’˜ĂđT5@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙UCompObj˙˙˙˙V\ObjInfo˙˙˙˙˙˙˙˙X€@ ƒk&\PV ŔČw ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` 2ƒfƒa–(–)†=ƒk†×2ƒgƒa–(–)Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙YD_990364205Œ›“ ŔFđT5@’˜ĂđT5@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙[CompObj’”˙˙˙˙\\ObjInfo˙˙˙˙•˙˙˙˙^Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙_d_990364350‡ž˜ ŔFđT5@’˜ĂđT5@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙a3Sţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€ˆ ƒfƒx–(–)†=ƒgƒx–(–)†×ƒhƒx–(–)€ €2 €Ť €„?Ó˙˙ÔĎ÷đ˜ţCompObj—™˙˙˙˙b\ObjInfo˙˙˙˙š˙˙˙˙dOle10Native˙˙˙˙˙˙˙˙˙˙˙˙eŒ_990364250˙˙˙˙  ŔFđT5@’˜ĂđT5@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙hCompObjœž˙˙˙˙i\ObjInfo˙˙˙˙Ÿ˙˙˙˙kOle10Native˙˙˙˙˙˙˙˙˙˙˙˙l„ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ 2ƒfƒa–(–)†š2ƒgƒa–(–)†×2ƒhƒa–(–)ss˙˙ŽŽyyî_990364349˙˙˙˙˙˙˙˙˘ ŔFđT5@’˜ĂŰ6@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙oCompObjĄŁ˙˙˙˙p\ObjInfo˙˙˙˙¤˙˙˙˙rţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€  2ƒfƒa–(–)†=ƒgƒa–(–)†×2ƒhƒa–(–)†+2ƒgƒa–(–)†×ƒhƒa–(–)-ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙s¤_990424141´Ż§ ŔFŰ6@’˜ĂŰ6@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙vCompObjŚ¨˙˙˙˙w\Equationô9˛q€€ ƒfƒx–(–)†=ˆ2ƒx†-ˆ6–(–) ˆ2 Z¤ţ˙˙N$*ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛qObjInfo˙˙˙˙Š˙˙˙˙yOle10Native˙˙˙˙˙˙˙˙˙˙˙˙z„_990423896˙˙˙˙˙˙˙˙Ź ŔFŰ6@’˜ĂŰ6@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙}CompObjŤ­˙˙˙˙~\ObjInfo˙˙˙˙Ž˙˙˙˙€Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙l_990424230˙˙˙˙˙˙˙˙ą ŔFŰ6@’˜ĂŰ6@’˜Ăţ˙˙˙‚ţ˙˙˙ţ˙˙˙…ţ˙˙˙ţ˙˙˙ˆ‰ţ˙˙˙ţ˙˙˙Œţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙’ţ˙˙˙ţ˙˙˙•–ţ˙˙˙ţ˙˙˙™ţ˙˙˙ţ˙˙˙œţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙Ł¤ţ˙˙˙ţ˙˙˙§ţ˙˙˙ŠŞŤŹţ˙˙˙Žţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙łţ˙˙˙ľśˇ¸ţ˙˙˙şţ˙˙˙ţ˙˙˙ţ˙˙˙žţ˙˙˙ŔÁÂĂÄĹĆţ˙˙˙Čţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙Íţ˙˙˙ţ˙˙˙ĐŃţ˙˙˙ţ˙˙˙Ôţ˙˙˙ţ˙˙˙×ţ˙˙˙ţ˙˙˙Úţ˙˙˙ţ˙˙˙Ýţ˙˙˙ţ˙˙˙ŕţ˙˙˙ţ˙˙˙ăţ˙˙˙ţ˙˙˙ćţ˙˙˙ţ˙˙˙éęëţ˙˙˙ţ˙˙˙îţ˙˙˙ţ˙˙˙ńňţ˙˙˙ţ˙˙˙őţ˙˙˙ţ˙˙˙řţ˙˙˙ţ˙˙˙űţ˙˙˙ţ˙˙˙ţţ˙˙˙ţ˙˙˙€h ƒfƒx–(–)†=‚s‚i‚nˆ2ƒx–(–)DI3ShrGhrGţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒfƒx–(–)†=ˆ6†-ˆ3ƒx–(–) Ole ˙˙˙˙˙˙˙˙˙˙˙˙ƒCompObj°˛˙˙˙˙„\ObjInfo˙˙˙˙ł˙˙˙˙†Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙‡„ˆ3 ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒfƒx–(–)†=‚c‚o‚sˆ3ƒx–(–)DI3S_990423905Şšś ŔFŰ6@’˜ĂŰ6@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ŠCompObjľˇ˙˙˙˙‹\ObjInfo˙˙˙˙¸˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙Žd_990423964˙˙˙˙˙˙˙˙ť ŔFŰ6@’˜ĂŰ6@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjşź˙˙˙˙‘\ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒfƒx–(–)†=ƒx ˆ2 †-ˆ1–(–) ˆ2’&ObjInfo˙˙˙˙˝˙˙˙˙“Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙”„_990424500ĽÜŔ ŔFŰ6@’˜ĂŰ6@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙—CompObjżÁ˙˙˙˙˜\ObjInfo˙˙˙˙Â˙˙˙˙šOle10Native˙˙˙˙˙˙˙˙˙˙˙˙›„_990424528˙˙˙˙˙˙˙˙Ĺ ŔFŰ6@’˜ĂŰ6@’˜Ăţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒfƒx–(–)†=ƒgƒhƒx–(–)–(–)ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Ole ˙˙˙˙˙˙˙˙˙˙˙˙žCompObjÄĆ˙˙˙˙Ÿ\ObjInfo˙˙˙˙Ç˙˙˙˙ĄOle10Native˙˙˙˙˙˙˙˙˙˙˙˙˘¤Equationô9˛q€  2ƒfƒa–(–)†=2ƒgƒhƒa–(–)–(–)†×2ƒhƒa–(–)L„„ÜÜčč_874776212+ŐĘŔFŰ6@’˜Ă0b8@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ĽPIC 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ƒfƒx–(–) Ole ˙˙˙˙˙˙˙˙˙˙˙˙ůCompObj˙˙˙˙ú\ObjInfo˙˙˙˙˙˙˙˙üOle10Native˙˙˙˙˙˙˙˙˙˙˙˙ýD_990425648đ ŔF0b8@’˜ĂĐč9@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙˙CompObj˙˙˙˙\ObjInfo˙˙˙˙˙˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙#$ţ˙˙˙ţ˙˙˙'ţ˙˙˙ţ˙˙˙*ţ˙˙˙ţ˙˙˙-ţ˙˙˙ţ˙˙˙0ţ˙˙˙ţ˙˙˙3ţ˙˙˙ţ˙˙˙67ţ˙˙˙ţ˙˙˙:ţ˙˙˙ţ˙˙˙=ţ˙˙˙ţ˙˙˙@ţ˙˙˙ţ˙˙˙CDţ˙˙˙ţ˙˙˙Gţ˙˙˙ţ˙˙˙JKţ˙˙˙ţ˙˙˙Nţ˙˙˙ţ˙˙˙QRţ˙˙˙ţ˙˙˙Uţ˙˙˙ţ˙˙˙Xţ˙˙˙ţ˙˙˙[ţ˙˙˙ţ˙˙˙^_ţ˙˙˙ţ˙˙˙bţ˙˙˙ţ˙˙˙eţ˙˙˙ţ˙˙˙hţ˙˙˙ţ˙˙˙kţ˙˙˙ţ˙˙˙nţ˙˙˙ţ˙˙˙qrţ˙˙˙ţ˙˙˙uţ˙˙˙ţ˙˙˙xyţ˙˙˙ţ˙˙˙|ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ 2ƒfƒx–(–)ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛qOle10Native˙˙˙˙˙˙˙˙˙˙˙˙D_990425810  ŔFĐč9@’˜ĂĐč9@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj  ˙˙˙˙\ObjInfo˙˙˙˙ ˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙ D_990425766˙˙˙˙˙˙˙˙ ŔFĐč9@’˜ĂĐč9@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ €@ 2ƒgˆ2–(–)ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒgƒx–(–)†=ƒfƒx–(–)–[–]CompObj˙˙˙˙ \ObjInfo˙˙˙˙˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙„_990425837˙˙˙˙˙˙˙˙ ŔFĐč9@’˜ĂĐč9@’˜Ă ˆ3˙˙˙˙˙˙˙˙˙˙˙Ŕ˙˙˙˙˙˙˙˙˙ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ 2ƒhˆ2–(–)Ole ˙˙˙˙˙˙˙˙˙˙˙˙CompObj˙˙˙˙\ObjInfo˙˙˙˙˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙D_990425854 " ŔFĐč9@’˜ĂĐč9@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj˙˙˙˙\ObjInfo˙˙˙˙˙˙˙˙ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒhƒx–(–)†=ƒfƒx ˆ3 –(–)Sţ˙ ˙˙˙˙ ŔFMathType Equation Equation Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙d_990425925˙˙˙˙˙˙˙˙ ŔFĐč9@’˜ĂĐč9@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj ˙˙˙˙\Equationô9˛q€€ 2ƒfƒx–(–)†=ƒxƒx ˆ2 †+ˆ1Times New Roman#-ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛qObjInfo˙˙˙˙!˙˙˙˙!Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙"„_990425963'$ ŔFĐč9@’˜ĂĐč9@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙%CompObj#%˙˙˙˙&\ObjInfo˙˙˙˙&˙˙˙˙(Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙)d_990425986˙˙˙˙˙˙˙˙) ŔFĐč9@’˜ĂĐč9@’˜Ă€` ƒgƒx–(–)†= ˆ3ƒx†-ˆ1 O Ŕ´DI3Sţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ 2ƒFƒx–(–)Ole ˙˙˙˙˙˙˙˙˙˙˙˙+CompObj(*˙˙˙˙,\ObjInfo˙˙˙˙+˙˙˙˙.Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙/Dţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€Œ ƒFƒx–(–)†=ƒfƒgƒx–(–)–(–) ˙˙˙Ëhý˙4vG4vG_990426003T. ŔFĐč9@’˜ĂĐč9@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙1CompObj-/˙˙˙˙2\ObjInfo˙˙˙˙0˙˙˙˙4Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙5_9904261836;3 ŔFĐč9@’˜ĂĐč9@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙8CompObj24˙˙˙˙9\ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒdƒdƒxƒfƒx–(–)–[–]DI3Sţ˙ ˙˙˙˙ ŔFMathType Equation Equation ObjInfo˙˙˙˙5˙˙˙˙;Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙<d_990426182˙˙˙˙˙˙˙˙8 ŔFĐč9@’˜ĂĐč9@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙>CompObj79˙˙˙˙?\ObjInfo˙˙˙˙:˙˙˙˙AOle10Native˙˙˙˙˙˙˙˙˙˙˙˙B„_990426462˙˙˙˙˙˙˙˙= ŔFĐč9@’˜ĂĐč9@’˜ĂEquationô9˛q€€ ƒdƒdƒxƒfˆ3ƒx–(–)–[–]†=ˆ6ƒx˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙ECompObj<>˙˙˙˙F\ObjInfo˙˙˙˙?˙˙˙˙HOle10Native˙˙˙˙˙˙˙˙˙˙˙˙I„€€ ƒfƒx–(–)†=ƒx ˆ2  ˆ2ƒx†-ˆ1 ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€_9904265041JB ŔFĐč9@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙LCompObjAC˙˙˙˙M\ObjInfo˙˙˙˙D˙˙˙˙OOle10Native˙˙˙˙˙˙˙˙˙˙˙˙P¤_990426581˙˙˙˙˙˙˙˙G ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙SCompObjFH˙˙˙˙T\  2ƒfƒx–(–)†=ƒxˆ3ƒx†-ˆ2–(–)ˆ2ƒx†-ˆ1–(–) )ˆ3ˆ2  űţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` 2ƒfˆ0–(–)†=ˆ0C7€C7°O Ŕ´ObjInfo˙˙˙˙I˙˙˙˙VOle10Native˙˙˙˙˙˙˙˙˙˙˙˙Wd_990426658EOL ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙YDI3Sţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€  2ƒfƒx–(–)†>ˆ0‚? ‚,2ƒfƒx–(–)†=ˆ0‚? ‚,2ƒfƒx–(–)†<ˆ0‚?˙˙˙˙˙˙˙˙˙˙˙˙˙˙CompObjKM˙˙˙˙Z\ObjInfo˙˙˙˙N˙˙˙˙\Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙]¤_990426720˙˙˙˙˙˙˙˙Q ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙`CompObjPR˙˙˙˙a\ObjInfo˙˙˙˙S˙˙˙˙cOle10Native˙˙˙˙˙˙˙˙˙˙˙˙dLţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€H ƒf^1PV ˜w  @kG@kGţ˙ ˙˙˙˙ ŔFMathType Equation Equation _990426792@|V ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙fCompObjUW˙˙˙˙g\ObjInfo˙˙˙˙X˙˙˙˙iEquationô9˛q€` ˆ4 ˆ3  ‚/ˆ9‚,†Ľ–[–]˙˙˙˙˙˙ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙jd_990426930˙˙˙˙˙˙˙˙[ ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙lCompObjZ\˙˙˙˙m\ObjInfo˙˙˙˙]˙˙˙˙oOle10Native˙˙˙˙˙˙˙˙˙˙˙˙p„_990426958Yc` ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙s€ ƒfƒx–(–)†=ƒx†-ˆ1–(–) )ˆ3ˆ2-đţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒgƒx–(–)†=ˆ1†-ƒx–(–) )CompObj_a˙˙˙˙t\ObjInfo˙˙˙˙b˙˙˙˙vOle10Native˙˙˙˙˙˙˙˙˙˙˙˙w„_990427009˙˙˙˙˙˙˙˙e ŔFpo;@’˜Ăpo;@’˜Ăˆ3ˆ2 ˙˙˙˙űţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€d 2ƒfˆ1–(–)†=ˆ0C7€C7tO Ŕ´DI3S<_G<_GOle ˙˙˙˙˙˙˙˙˙˙˙˙zCompObjdf˙˙˙˙{\ObjInfo˙˙˙˙g˙˙˙˙}Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙~h_990427040^rj ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙€CompObjik˙˙˙˙\ObjInfo˙˙˙˙l˙˙˙˙ƒţ˙˙˙‚ţ˙˙˙ţ˙˙˙…ţ˙˙˙ţ˙˙˙ˆţ˙˙˙ţ˙˙˙‹ţ˙˙˙ţ˙˙˙Žţ˙˙˙ţ˙˙˙‘’ţ˙˙˙ţ˙˙˙•ţ˙˙˙ţ˙˙˙˜™ţ˙˙˙ţ˙˙˙œţ˙˙˙ţ˙˙˙Ÿ ţ˙˙˙ţ˙˙˙Łţ˙˙˙ţ˙˙˙Śţ˙˙˙ţ˙˙˙Šţ˙˙˙ţ˙˙˙Źţ˙˙˙ţ˙˙˙Żţ˙˙˙ţ˙˙˙˛łţ˙˙˙ţ˙˙˙śţ˙˙˙ţ˙˙˙šşţ˙˙˙ţ˙˙˙˝ţ˙˙˙ţ˙˙˙ŔÁţ˙˙˙ţ˙˙˙Äţ˙˙˙ţ˙˙˙Çţ˙˙˙ţ˙˙˙Ęţ˙˙˙ţ˙˙˙Íţ˙˙˙ţ˙˙˙Đţ˙˙˙ţ˙˙˙Óţ˙˙˙ţ˙˙˙Öţ˙˙˙ţ˙˙˙Ůţ˙˙˙ţ˙˙˙Üţ˙˙˙ţ˙˙˙ßŕţ˙˙˙ţ˙˙˙ăţ˙˙˙ţ˙˙˙ćçţ˙˙˙ţ˙˙˙ęţ˙˙˙ţ˙˙˙íţ˙˙˙ţ˙˙˙đţ˙˙˙ţ˙˙˙óţ˙˙˙ţ˙˙˙öţ˙˙˙ţ˙˙˙ůúţ˙˙˙ţ˙˙˙ýţ˙˙˙ţ˙˙˙ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€d 2ƒgˆ1–(–)†=ˆ0C7€C7`O §DI3SŹ|Gţ˙ ˙˙˙˙ ŔFMathType Equation Equation Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙„h_990427073˙˙˙˙˙˙˙˙o ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙†CompObjnp˙˙˙˙‡\Equationô9˛q€@ ƒh†=ƒf†+ƒgw ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€ObjInfo˙˙˙˙q˙˙˙˙‰Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙ŠD_990427097mt ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ŒCompObjsu˙˙˙˙\ObjInfo˙˙˙˙v˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙¤_990427171˙˙˙˙˙˙˙˙y ŔFpo;@’˜Ăpo;@’˜Ă  2ƒhˆ1–(–)†='‚l‚i‚m ƒx†Žˆ1 ƒhƒx–(–)†-ƒhˆ1–(–)ƒx†-ˆ1ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ 2ƒhˆ1–(–)†=2ƒfˆ1–(–)†+2ƒgOle ˙˙˙˙˙˙˙˙˙˙˙˙“CompObjxz˙˙˙˙”\ObjInfo˙˙˙˙{˙˙˙˙–Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙—„ˆ1–(–)†=ˆ0Gţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒhƒx–(–)†=ƒfƒx–(–)†×ƒgƒx–(–)˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙_990427913h~ ŔFpo;@’˜Ăpo;@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙šCompObj}˙˙˙˙›\ObjInfo˙˙˙˙€˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙ž„_990427879w†ƒ ŔFö<@’˜Ăö<@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ĄCompObj‚„˙˙˙˙˘\ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒf:HV ˜w ObjInfo˙˙˙˙…˙˙˙˙¤Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙ĽD_990427889˙˙˙˙˙˙˙˙ˆ ŔFö<@’˜Ăö<@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙§CompObj‡‰˙˙˙˙¨\ObjInfo˙˙˙˙Š˙˙˙˙ŞOle10Native˙˙˙˙˙˙˙˙˙˙˙˙ŤD_990428276¤˙˙˙˙ ŔFö<@’˜Ăö<@’˜Ăţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒg:HV ˜w ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙­CompObjŒŽ˙˙˙˙Ž\ObjInfo˙˙˙˙˙˙˙˙°Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙ą„€€ ƒh†-ˆ2–(–) and ƒhˆ3–(–)!€d€€œ˙€€ü„?B˙˙ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€_990428394šX’ ŔFö<@’˜Ăö<@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙´CompObj‘“˙˙˙˙ľ\ObjInfo˙˙˙˙”˙˙˙˙ˇOle10Native˙˙˙˙˙˙˙˙˙˙˙˙¸„_990427931˙˙˙˙Ÿ— ŔFö<@’˜Ăö<@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ťCompObj–˜˙˙˙˙ź\€ 2ƒh†-ˆ2–(–) and 2ƒhˆ3–(–)Symbol-đţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒhƒx–(–)†=ƒfƒgƒx–(–)–(ObjInfo˙˙˙˙™˙˙˙˙žOle10Native˙˙˙˙˙˙˙˙˙˙˙˙ż„_990428067•‹œ ŔFö<@’˜Ăö<@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙–)td€ow€em€)€˙˙€˙˙„?ES˙˙O ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ 2ƒhˆ3–(–)CompObj›˙˙˙˙Ă\ObjInfo˙˙˙˙ž˙˙˙˙ĹOle10Native˙˙˙˙˙˙˙˙˙˙˙˙ĆD_990428066˙˙˙˙˙˙˙˙Ą ŔFö<@’˜Ăö<@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ČCompObj ˘˙˙˙˙É\ObjInfo˙˙˙˙Ł˙˙˙˙ËOle10Native˙˙˙˙˙˙˙˙˙˙˙˙Ědţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` 2ƒh†-ˆ1–(–)V C7€C7O ŕ­DI3Sţ˙ ˙˙˙˙ ŔFMathType Equation Equation _990428112˙˙˙˙˙˙˙˙Ś ŔFö<@’˜Ăö<@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ÎCompObjĽ§˙˙˙˙Ď\ObjInfo˙˙˙˙¨˙˙˙˙ŃEquationô9˛q€@ 2ƒhˆ1–(–)ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙ŇD_977840241˙˙˙˙˙˙˙˙Ť ŔFö<@’˜Ăö<@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ÔCompObjŞŹ˙˙˙˙Ő\ObjInfo˙˙˙˙­˙˙˙˙×Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙Řd_977840554˙˙˙˙˙˙˙˙° ŔFö<@’˜Ăö<@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙Ú` ƒx ˆ2 †+ƒy ˆ2 †=ˆ2ˆ53×ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒf ˆ1 ƒx–(–)†= ˆ2ˆ5†-ƒx ˆ2˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙CompObjŻą˙˙˙˙Ű\ObjInfo˙˙˙˙˛˙˙˙˙ÝOle10Native˙˙˙˙˙˙˙˙˙˙˙˙Ţ„_977840553bŽľ ŔFö<@’˜Ăö<@’˜Ăţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒf ˆ2 ƒx–(–)†=†- ˆ2ˆ5†-ƒx ˆ2ŒFţOle ˙˙˙˙˙˙˙˙˙˙˙˙áCompObj´ś˙˙˙˙â\ObjInfo˙˙˙˙ˇ˙˙˙˙äOle10Native˙˙˙˙˙˙˙˙˙˙˙˙ĺ„_977840668łÂş ŔF°|>@’˜Ă°|>@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙čCompObjšť˙˙˙˙é\ObjInfo˙˙˙˙ź˙˙˙˙ëţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒf ˆ1w ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙ěD_977840683˙˙˙˙˙˙˙˙ż ŔF°|>@’˜Ă°|>@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙îCompObjžŔ˙˙˙˙ď\Equationô9˛q€@ ƒf ˆ2w ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€ObjInfo˙˙˙˙Á˙˙˙˙ńOle10Native˙˙˙˙˙˙˙˙˙˙˙˙ňD_977840767˝ÇÄ ŔF°|>@’˜Ă°|>@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ôCompObjĂĹ˙˙˙˙ő\ObjInfo˙˙˙˙Ć˙˙˙˙÷Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙ř„_977840818˙˙˙˙˙˙˙˙É ŔF°|>@’˜Ă°|>@’˜Ă€ ƒx ˆ2 †+ƒf ˆ1 ƒx–(–)–(–) ˆ2 †=ˆ2ˆ5˙ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€€ ƒx ˆ2 †+ˆ2ˆ5†-ƒx ˆ2 –(Ole ˙˙˙˙˙˙˙˙˙˙˙˙űCompObjČĘ˙˙˙˙ü\ObjInfo˙˙˙˙Ë˙˙˙˙ţOle10Native˙˙˙˙˙˙˙˙˙˙˙˙˙„ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙"ţ˙˙˙ţ˙˙˙%ţ˙˙˙ţ˙˙˙(ţ˙˙˙ţ˙˙˙+ţ˙˙˙ţ˙˙˙.ţ˙˙˙ţ˙˙˙1ţ˙˙˙ţ˙˙˙4ţ˙˙˙ţ˙˙˙7ţ˙˙˙ţ˙˙˙:ţ˙˙˙ţ˙˙˙=ţ˙˙˙ţ˙˙˙@ţ˙˙˙ţ˙˙˙Cţ˙˙˙ţ˙˙˙Fţ˙˙˙ţ˙˙˙Iţ˙˙˙ţ˙˙˙Lţ˙˙˙ţ˙˙˙Oţ˙˙˙ţ˙˙˙Rţ˙˙˙ţ˙˙˙Uţ˙˙˙ţ˙˙˙Xţ˙˙˙ţ˙˙˙[\ţ˙˙˙ţ˙˙˙_ţ˙˙˙ţ˙˙˙bţ˙˙˙ţ˙˙˙eţ˙˙˙ţ˙˙˙hţ˙˙˙ţ˙˙˙kţ˙˙˙ţ˙˙˙nţ˙˙˙ţ˙˙˙qţ˙˙˙ţ˙˙˙tţ˙˙˙ţ˙˙˙wţ˙˙˙yz{|}~ţ˙˙˙€–)†=ˆ2ˆ5ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒx ˆ2 †+ƒy ˆ2 †+ˆ1†=ˆ0ŔëDI3S_977841183¸ôÎ ŔF°|>@’˜Ă°|>@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjÍĎ˙˙˙˙\ObjInfo˙˙˙˙Đ˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙d_977841377˙˙˙˙˙˙˙˙Ó ŔF°|>@’˜Ă°|>@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjŇÔ˙˙˙˙ \ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒx ˆ2 †+ƒy ˆ2 †=†-ˆ1O ŔëDI3Sţ˙ ˙˙˙˙ ŔFMathType Equation Equation ObjInfo˙˙˙˙Ő˙˙˙˙ Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙ d_977841540ŃŰŘ ŔF°|>@’˜Ă°|>@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj×Ů˙˙˙˙\ObjInfo˙˙˙˙Ú˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙D_977841548˙˙˙˙˙˙˙˙Ý ŔF°|>@’˜Ă°|>@’˜ĂEquationô9˛q€@ ƒx†1 V łw ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€Ole ˙˙˙˙˙˙˙˙˙˙˙˙CompObjÜŢ˙˙˙˙\ObjInfo˙˙˙˙ß˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙D@ ƒyŚ1V łw ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒx†1 V łw _977841582Öęâ ŔF°|>@’˜Ă°|>@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjáă˙˙˙˙\ObjInfo˙˙˙˙ä˙˙˙˙Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙D_977842735˙˙˙˙˙˙˙˙ç ŔF°|>@’˜Ă°|>@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ CompObjćč˙˙˙˙!\ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒxƒy†-ˆ2ƒy†-ˆ5ƒx†=ˆ0€C7tO €ůDI3Sţ˙ ˙˙˙˙ ŔFMathType Equation Equation ObjInfo˙˙˙˙é˙˙˙˙#Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙$d_977842819ĺďě ŔFP@@’˜ĂP@@’˜ĂOle 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pRLřÍ:,Œr/Łţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ ţ˙˙˙"ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙'ţ˙˙˙)*+,-./0123ţ˙˙˙5ţ˙˙˙ţ˙˙˙8ţ˙˙˙ţ˙˙˙;ţ˙˙˙=>?@ABCDEFţ˙˙˙Hţ˙˙˙ţ˙˙˙Kţ˙˙˙ţ˙˙˙Nţ˙˙˙PQRSţ˙˙˙Uţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙Zţ˙˙˙\]^_`abcdefghiţ˙˙˙kţ˙˙˙ţ˙˙˙nţ˙˙˙ţ˙˙˙qţ˙˙˙stuvwxyz{|}ţ˙˙˙ţ˙˙˙ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛q3ןfI aI 2ƒf˙˙˙ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qObjInfo˙˙˙˙u˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙0_920393942˙˙˙˙˙˙˙˙xÎŔFĐF@’˜ĂĐF@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjwy˙˙˙˙fObjInfo˙˙˙˙z˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙,_920393965âĚ}ÎŔF0—D@’˜Ă0—D@’˜Ă3×x{I yI ƒfţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛q3×x{I yI ƒfţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS EqOle ˙˙˙˙˙˙˙˙˙˙˙˙ CompObj|~˙˙˙˙ fObjInfo˙˙˙˙˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ ,_920394009˙˙˙˙˙˙˙˙‚ÎŔFĐF@’˜ĂĐF@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjƒ˙˙˙˙fObjInfo˙˙˙˙„˙˙˙˙uation Equation.3ô9˛q3×_I”QI †d" ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛q3×_I”QI †d" Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙,_920394050€ł‡ÎŔFĐF@’˜ĂĐF@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj†ˆ˙˙˙˙fObjInfo˙˙˙˙‰˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙,_915022642˙˙˙˙˙˙˙˙ŒŔFĐF@’˜ĂĐF@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙Lží|ččží Ż ˙˙˙.1  Ŕ`&˙˙˙˙Ŕ˙˙˙Đ˙˙˙  & MathType ű@ţSymbol- 2 €4łöű@ţTimes New Roman)-đ 2 €m1ŕ & ˙˙˙˙űźPIC ‹Ž˙˙˙˙LMETA ˙˙˙˙˙˙˙˙˙˙˙˙hCompObj˙˙˙˙!fObjInfo˙˙˙˙˙˙˙˙#"Systemn-đ ţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q”ŐčqJ0mJLrJ †łˆ1LC Œô”ččEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙$,_915273404^­“ŔFĐF@’˜ĂĐF@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙%PIC ’•˙˙˙˙&LMETA ˙˙˙˙˙˙˙˙˙˙˙˙(ÜCompObj”–˙˙˙˙4fObjInfo˙˙˙˙—˙˙˙˙6Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙7\C Œ j ˙˙˙.1    &˙˙˙˙Ŕ˙˙˙°˙˙˙ŕ Đ & MathTypeĐű@ţTimes New Roman- 2 €NF 2 €FxÄ 2 €—f} 2 €-t} 2 €o dtŕ}ű ˙Times New Roman-đ 2 ř›xbű@ţTimes New Roman-đ 2 €‰(“ 2 €)“ 2 €Œ(“ 2 €Î)“ű@ţSymbol-đ 2 €=ö 2 ʇňtű ˙Times New Roman-đ 2 Ů”1p & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q”Ő@čqJ0mJLrJ ƒF‚(ƒx‚)†=ƒf‚(ƒt‚)ƒdƒt ˆ1ƒx †ňLë žä|ččë ž N ˙˙˙.1  `  &˙˙˙˙Ŕ˙˙˙ą˙˙˙`  & MathTypePű@ţTimes 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řxbű@ţTimes New Roman-đ 2 €‰(“ 2 €)“ű@ţSymbol-đ 2 €=ö 2 €j +ö 2 Ę˝ňtű ˙Times New Roman-đ 2 ˇ]2p 2 ŮĘ1p 2 ř€2pű@ţTimes New Roman!-đ 2 €Š 1ŕ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q”ŐXčqJ0mJLrJ ƒF‚(ƒx‚)†= ƒt ˆ2 †+ˆ1 ˆ1ˆ2ƒx †ň ƒdƒtEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙mt_915274037ŸÉŻŔFp¤G@’˜Ăp¤G@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙oPIC Žą˙˙˙˙pLLMN$ŕččMN _ ˙˙˙.1   &˙˙˙˙Ŕ˙˙˙°˙˙˙`° & MathType° ú"-Ř/¸çű@ţTimes New Romanl- 2  Nlim}}] 2  7(“ 2  Í)“ű ˙Times New Roman!-đ 2 €GxbMETA ˙˙˙˙˙˙˙˙˙˙˙˙rČCompObj°˛˙˙˙˙~fObjInfo˙˙˙˙ł˙˙˙˙€Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙\ű@ţTimes New Romanl-đ 2  üF 2  ôxÄű ˙Symbol-đ 2 €ˇŽÝű ˙Times New Romanl-đ 2 €1p 2 €=2p & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qţ˙˙˙‚ţ˙˙˙ţ˙˙˙…ţ˙˙˙‡ˆ‰Šţ˙˙˙Œţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙‘ţ˙˙˙“”•–ţ˙˙˙˜ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙Ÿ Ą˘Ł¤ĽŚ§¨ŠŞţ˙˙˙Źţ˙˙˙ţ˙˙˙Żţ˙˙˙ţ˙˙˙˛ţ˙˙˙´ľśˇ¸šşťźţ˙˙˙žţ˙˙˙ţ˙˙˙Áţ˙˙˙ţ˙˙˙Äţ˙˙˙ĆÇČÉĘËĚÍÎţ˙˙˙Đţ˙˙˙ţ˙˙˙Óţ˙˙˙ţ˙˙˙Öţ˙˙˙ŘŮÚŰÜÝŢţ˙˙˙ŕţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ĺţ˙˙˙çčéęëěíîţ˙˙˙đţ˙˙˙ţ˙˙˙óţ˙˙˙ţ˙˙˙öţ˙˙˙ţ˙˙˙ůţ˙˙˙ţ˙˙˙üţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙”Ő@čqJ0mJLrJ '‚l‚i‚m ƒx†Ž)ˆ1ˆ2 ƒF‚(ƒx‚)L„ĘÜčý„Ę ‰ ˙˙˙.1   `&˙˙˙˙Ŕ˙˙˙đ˙˙˙ _915274093˙˙˙˙˙˙˙˙śŔFp¤G@’˜Ăp¤G@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ƒPIC ľ¸˙˙˙˙„LMETA ˙˙˙˙˙˙˙˙˙˙˙˙† & MathType ű@ţSymbol- 2 `4Łö & ˙˙˙˙űź"Systemn-đHţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q”Ő čqJ0mJLrJ †ŁCompObjˇš˙˙˙˙‹fObjInfo˙˙˙˙ş˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ž(_915274107´Â˝ŔFp¤G@’˜Ăp¤G@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙PIC źż˙˙˙˙LMETA ˙˙˙˙˙˙˙˙˙˙˙˙’CompObjžŔ˙˙˙˙—fL„ĘÜčý„Ę ‰ ˙˙˙.1   `&˙˙˙˙Ŕ˙˙˙đ˙˙˙  & MathType ű@ţSymbol- 2 `4Łö & ˙˙˙˙űź"Systemn-đHţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q”Ő čqJ0mJLrJ †ŁLŠ ŇźččŠ Ň Œ ˙˙˙.1  `` &˙˙˙˙Ŕ˙˙˙¤˙˙˙ ObjInfo˙˙˙˙Á˙˙˙˙™Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙š(_915275212˙˙˙˙˙˙˙˙ÄŔFp¤G@’˜Ă+I@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙›PIC ĂĆ˙˙˙˙œLMETA ˙˙˙˙˙˙˙˙˙˙˙˙ž CompObjĹÇ˙˙˙˙ŤfObjInfo˙˙˙˙Č˙˙˙˙­ & MathTypeĐ ú"-T@Tű@ţTimes New Roman - 2 ŹŚdŕ 2 RdxŕÄ 2 ŔÜuŕ 2 Ŕd duŕŕű ˙Times New Roman-đ 2 8rxbű@ţTimes New Roman -đ 2 Ŕcos(Äஓ 2 ŔĂ)“ 2 Ŕ 2ŕű ˙Times New Roman-đ 2 k0pű@ţSymbol-đ 2 Ŕćpöű@ţSymbol-đ 2 ^ňt & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q”ŐPčqJ0mJLrJ ƒdƒdƒx‚c‚o‚s‚(ˆ2„pƒu‚)ƒdƒu ˆ0ƒx †ňEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙Žl_915275279ťqËŔF+I@’˜Ă+I@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙°PIC ĘÍ˙˙˙˙ąLLöŔĐččö  ˙˙˙.1  €&˙˙˙˙Ŕ˙˙˙¤˙˙˙Ŕ$ & MathTypeŕ ú"-T@Tcű@ţTimes New Romanh- 2 Źč1ŕ 2 R2ŕű@ţSymbol-META ˙˙˙˙˙˙˙˙˙˙˙˙łDCompObjĚÎ˙˙˙˙˝fObjInfo˙˙˙˙Ď˙˙˙˙żEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙ŔDđ 2 +pöű@ţTimes New Romanh-đ 2 ŔsinŽ}ŕű@ţTimes New Roman-đ 2 ŔëxÄ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q”Ő(ÔlJPqJ8mJ ˆ1ˆ2„p‚s‚i‚nƒxL ö´Đčč ö : ˙˙˙.1  € &˙˙˙˙Ŕ˙˙˙¤˙˙˙ŕ$ & MathTypeŕ ú"-T@_915275355˙˙˙˙˙˙˙˙ŇŔF+I@’˜Ă+I@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ÂPIC ŃÔ˙˙˙˙ĂLMETA ˙˙˙˙˙˙˙˙˙˙˙˙Ĺ|Tcű@ţTimes New Romanh- 2 Źč1ŕ 2 !R2ŕ 2 Ŕ“2ŕű@ţSymbol-đ 2 !+pö 2 Ŕlpöű@ţTimes New Romanh-đ 2 Ŕ cos(Äஓ 2 Ŕ;)“ű@ţTimes New Roman -đ 2 ŔbxÄ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS EqCompObjÓŐ˙˙˙˙ĎfObjInfo˙˙˙˙Ö˙˙˙˙ŃEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙ŇP_915275402ĐďŮŔF+I@’˜Ă+I@’˜Ăuation Equation.2ô9˛q”Ő4ÔlJPqJ8mJ ˆ1ˆ2„p‚c‚o‚s‚(ˆ2„pƒx‚)LMW$TččMW ë ˙˙˙.Ole ˙˙˙˙˙˙˙˙˙˙˙˙ÔPIC ŘŰ˙˙˙˙ŐLMETA ˙˙˙˙˙˙˙˙˙˙˙˙×ŕCompObjÚÜ˙˙˙˙ßf1    &˙˙˙˙Ŕ˙˙˙Đ˙˙˙`đ & MathTypePű@ţTimes New Romanh- 2 €2cos(Äஓ 2 €Í)“ 2 €%2ŕű@ţSymbol-đ 2 €ţpöű@ţTimes New Romanh-đ 2 €ôxÄ & ˙˙˙˙űź"Systemn-đPrţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q”Ő$ĚlJHqJ0mJ ‚c‚o‚s‚(ˆ2„pƒx‚) LČ WŒTččČ W  ˙˙˙.1   ŕ&˙˙˙˙Ŕ˙˙˙Đ˙˙˙ đObjInfo˙˙˙˙Ý˙˙˙˙áEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙â@_915275427˙˙˙˙˙˙˙˙ŕŔF+I@’˜Ă+I@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ăPIC ßâ˙˙˙˙äLMETA ˙˙˙˙˙˙˙˙˙˙˙˙ć<CompObjáă˙˙˙˙ďfObjInfo˙˙˙˙ä˙˙˙˙ń & MathTypePű@ţTimes New Romanh- 2 €22ŕ 2 €P2ŕű@ţSymbol-đ 2 € pö 2 €)pöű@ţTimes New Romanh-đ 2 €]cos(Äஓ 2 €ř)“ű@ţTimes New Roman<í-đ 2 €xÄ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q”Ő(ĚlJHqJ0mJ ˆ2„p‚c‚o‚s‚(ˆ2„pƒx‚)ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙ňD_938247100˙˙˙˙˙˙˙˙çÎŔF+I@’˜Ă+I@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ôCompObjćč˙˙˙˙őfObjInfo˙˙˙˙é˙˙˙˙÷Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ř€_938247216 ôěÎŔF+I@’˜Ă°ąJ@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙úôÚd`hIDcI ƒf‚(ƒx‚)ƒdƒx†=ƒF‚(ƒb‚)†"ƒF‚(ƒa‚) ƒaƒb †+"ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚ”‚I´\I ƒF CompObjëí˙˙˙˙űfObjInfo˙˙˙˙î˙˙˙˙ýEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙ţ,_938247239˙˙˙˙˙˙˙˙ńÎŔF°ąJ@’˜Ă°ąJ@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙˙CompObjđň˙˙˙˙fObjInfo˙˙˙˙ó˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙,ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙$ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙)ţ˙˙˙ţ˙˙˙,-ţ˙˙˙ţ˙˙˙0ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙5ţ˙˙˙ţ˙˙˙8ţ˙˙˙ţ˙˙˙;ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙@ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙Eţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙Jţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙Oţ˙˙˙ţ˙˙˙RSţ˙˙˙ţ˙˙˙Vţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙[ţ˙˙˙ţ˙˙˙^ţ˙˙˙ţ˙˙˙aţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙fţ˙˙˙ţ˙˙˙ijţ˙˙˙ţ˙˙˙mţ˙˙˙ţ˙˙˙pţ˙˙˙ţ˙˙˙sţ˙˙˙ţ˙˙˙vwţ˙˙˙ţ˙˙˙zţ˙˙˙ţ˙˙˙}ţ˙˙˙ţ˙˙˙€ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚŒlIŹRI ƒfţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛q_938247299ďůöÎŔF°ąJ@’˜Ă°ąJ@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObjő÷˙˙˙˙fObjInfo˙˙˙˙ř˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙€_938248303˙˙˙˙˙˙˙˙űÎŔF°ąJ@’˜Ă°ąJ@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ CompObjúü˙˙˙˙ fôÚd¨tI\oI ƒdƒdƒxƒf‚(ƒt‚)ƒdƒt ƒaƒx †+" †=ƒf‚(ƒx‚)ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚ¨`hIDcI ƒdƒdƒxƒf‚(ƒt‚)ƒdƒt ƒaƒg‚(ƒx‚) †+" †=ƒf‚ObjInfo˙˙˙˙ý˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ä_938248822{&ÎŔF°ąJ@’˜Ă°ąJ@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙(ƒg‚(ƒx‚)‚)†Ĺ"ƒg ‚' ƒx–(–)ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚ`hIDcI ƒmƒyƒsƒtCompObj˙˙˙˙˙fObjInfo˙˙˙˙˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙8_938248859˙˙˙˙˙˙˙˙ÎŔF°ąJ@’˜Ă°ąJ@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj˙˙˙˙fObjInfo˙˙˙˙˙˙˙˙Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙xţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚ\ô{I\|I ƒmƒyƒsƒt‚(ƒx‚)†=ˆ1ƒt ˆ1ƒx †+" ƒdƒtţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛q_938248907  ÎŔF°ąJ@’˜Ă°ąJ@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙CompObj  ˙˙˙˙fObjInfo˙˙˙˙ ˙˙˙˙ ôÚ`hIDcI ƒmƒyƒsƒteţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚ`hIDcI ƒfEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙!8_938249308˙˙˙˙˙˙˙˙ÎŔFP8L@’˜ĂP8L@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙"CompObj˙˙˙˙#fObjInfo˙˙˙˙˙˙˙˙%Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙&,_938249364ÎŔFP8L@’˜ĂP8L@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙'CompObj˙˙˙˙(fObjInfo˙˙˙˙˙˙˙˙*Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙+œ_938249478!ÎŔFP8L@’˜ĂP8L@’˜Ăţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôڀl{Iź{I ƒh‚(ƒx‚)†=ƒf ˆ1ƒx †+" ‚(ƒt‚)ƒdƒt  for  ˆ1†d"ƒx†d"ˆ7ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Eqý˙˙˙ƒ…„†ˆ‡‰‹ŠŒŽ‘“’”ÖŐ–—˜™š›œžŸ Ą˘Ł¤ĽŚ§¨ŠŞŤŹ­ŽŻ°ą˛ł´ľśˇ¸šşťź˝žżŔÁÂĂÄĹĆÇČÉĘËĚÍÎĎĐŃŇÓÔő×ŘŮŰÚÜŢßáŕâäăĺçćčęéëěíďîđňńőóôö÷řůűúüý˙ţOle ˙˙˙˙˙˙˙˙˙˙˙˙.CompObj˙˙˙˙/fObjInfo˙˙˙˙˙˙˙˙1Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙2<uation Equation.3ô9˛qôÚ 4[Ip I ƒhˆ1–(–)ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚ0TŽIȀI ƒh ‚' ˆ4_938249449˙˙˙˙˙˙˙˙ÎŔFP8L@’˜ĂP8L@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙3CompObj˙˙˙˙4fObjInfo˙˙˙˙ ˙˙˙˙6Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙7L_938249523˙˙˙˙˙˙˙˙#ÎŔFP8L@’˜ĂP8L@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙9CompObj"$˙˙˙˙:f–(–)ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚŹI\oI ƒhţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS EqObjInfo˙˙˙˙%˙˙˙˙<Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙=,_938249559:(ÎŔFP8L@’˜ĂP8L@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙>CompObj')˙˙˙˙?fObjInfo˙˙˙˙*˙˙˙˙AEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙B,_938250260˙˙˙˙˙˙˙˙-ÎŔFP8L@’˜ĂđžM@’˜Ăuation Equation.3ô9˛qôÚŹI\oI ƒhţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚ`hIDcI ƒfomaOle ˙˙˙˙˙˙˙˙˙˙˙˙CCompObj,.˙˙˙˙DfObjInfo˙˙˙˙/˙˙˙˙FEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙G,_938250327+52ÎŔFđžM@’˜ĂđžM@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙HCompObj13˙˙˙˙IfObjInfo˙˙˙˙4˙˙˙˙Kţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚ`hIDcI ƒfţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙L,_938250464˙˙˙˙˙˙˙˙7ÎŔFđžM@’˜ĂđžM@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙MCompObj68˙˙˙˙NfObjInfo˙˙˙˙9˙˙˙˙PEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙Q„_9382505000D<ÎŔFđžM@’˜ĂđžM@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙TôÚhl{Iź{I ƒh‚(ƒx‚)†=ƒf ˆ0ƒxˆ2†+ˆ3 †+" ‚(ƒt‚)ƒdƒt ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qCompObj;=˙˙˙˙UfObjInfo˙˙˙˙>˙˙˙˙WEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙X,_938250527˙˙˙˙˙˙˙˙AÎŔFđžM@’˜ĂđžM@’˜ĂôÚ0’IôiI ƒh ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚ0ä˘I4ŁI ƒh ‚' ˆ2–(–)Ole ˙˙˙˙˙˙˙˙˙˙˙˙YCompObj@B˙˙˙˙ZfObjInfo˙˙˙˙C˙˙˙˙\Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙]L_938250579?NFÎŔFđžM@’˜ĂđžM@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙_CompObjEG˙˙˙˙`fObjInfo˙˙˙˙H˙˙˙˙bţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚlŽI\oI ƒh‚(ƒx‚)ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation 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" # $ % ţ˙˙˙' ţ˙˙˙ţ˙˙˙* ţ˙˙˙ţ˙˙˙- ţ˙˙˙ţ˙˙˙0 ţ˙˙˙ţ˙˙˙3 ţ˙˙˙5 6 7 8 9 : ; < = > ? @ A ţ˙˙˙C ţ˙˙˙ţ˙˙˙F G ţ˙˙˙ţ˙˙˙J ţ˙˙˙ţ˙˙˙M ţ˙˙˙ţ˙˙˙P ţ˙˙˙R S T U V W X Y Z [ ţ˙˙˙] ţ˙˙˙ţ˙˙˙` ţ˙˙˙ţ˙˙˙c ţ˙˙˙ţ˙˙˙f ţ˙˙˙ţ˙˙˙i ţ˙˙˙k l m n o p q r s t u v ţ˙˙˙x ţ˙˙˙ţ˙˙˙{ ţ˙˙˙ţ˙˙˙~ ţ˙˙˙€  p 2 €1 p 2 €e p 2 €D=ú 2 €Ż 0pŕű@ţSymbol-đ 2 €Ü+ö & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛q˘Ô(ÔlJPqJ8mJ ƒy‚" †+ ƒy = 0LgŇĂźččgŇ  ˙˙˙.1  ` &˙˙˙˙Ŕ˙˙˙¤˙˙˙` & MathTypeĐ ú"-T@Tű@ţTimes New Roman)- 2 ŹR_914661449˙˙˙˙˙˙˙˙˛ŔFpŮS@’˜Ă`U@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ PIC ą´˙˙˙˙ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ ,dyŕÄ 2 RdxŕÄ 2 Ŕ8f} 2 ŔęxÄű@ţSymbol-đ 2 ŔŠ=öű@ţTimes New Roman)-đ 2 Ŕ-(“ 2 ŔĂ)“ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qCompObjłľ˙˙˙˙ fObjInfo˙˙˙˙ś˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ L_914661605˘ĎšŔF`U@’˜Ă`U@’˜ĂŐ0čqJ0mJLrJ ƒdƒyƒdƒx†=ƒf‚(ƒx‚)L‚ Ňdźčč‚ Ň   ˙˙˙.1  ` &˙˙˙˙Ŕ˙˙˙¤˙˙˙` & MathTypeĐ ú"-T@Ole ˙˙˙˙˙˙˙˙˙˙˙˙ PIC ¸ť˙˙˙˙ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ $CompObjşź˙˙˙˙& fTű@ţTimes New Romanl- 2 ŹRdyŕÄ 2 RdxŕÄ 2 ŔóxÄű@ţSymbol-đ 2 ŔŠ=öű@ţTimes New Romanl-đ 2 Ŕäcos(Äஓ 2 ŔĚ)“ & ˙˙˙˙űź"Systemn-đGţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qObjInfo˙˙˙˙˝˙˙˙˙( Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙) P_1014542553˙˙˙˙˙˙˙˙Ŕ ŔF`U@’˜Ă`U@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙+ Ő4čqJ0mJLrJ ƒdƒyƒdƒx†=‚c‚o‚s‚(ƒx‚)ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒy†=‚s‚i‚nƒx–(–)†+ƒcxO űCompObjżÁ˙˙˙˙, \ObjInfo˙˙˙˙Â˙˙˙˙. Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙/ d_914661840˙˙˙˙˙˙˙˙ĹŔF`U@’˜Ă`U@’˜ĂDI3SLb Ň\źččb Ň Ł ˙˙˙.1  ``&˙˙˙˙Ŕ˙˙˙¤˙˙˙  & MathTypeĐ ú"-T@TTÎT ű@ţTimes New RomanOle ˙˙˙˙˙˙˙˙˙˙˙˙1 PIC ÄÇ˙˙˙˙2 LMETA ˙˙˙˙˙˙˙˙˙˙˙˙4 PCompObjĆČ˙˙˙˙B f- 2 ŹRdyŕÄ 2 RdxŕÄ 2 ŔóxÄ 2 Ŕ­yÄ 2 Ŕ.xÄű@ţSymbol-đ 2 ŔŠ=ö 2 Ŕĺ=ö 2 Ŕf=öű@ţTimes New Roman-đ 2 Ŕäcos(Äஓ 2 ŔĚ)“2 Ŕ{ and thpppÄŕŕpp}ŕ 2 ŔŒat Ä}pp2 Ŕ when pBŕÄŕpp 2 Ŕ?3ŕ 2 ü2ŕű@ţSymbol-đ 2 ŹŇpö & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐčqJ0mJLrJ ƒdƒyƒdƒx†=‚c‚o‚s‚(ƒx‚)   and  that  ƒy†=ˆ3 when  ƒx†=„pˆ2ObjInfo˙˙˙˙É˙˙˙˙D Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙E Ź_1014542598žÖĚ ŔF`U@’˜Ă`U@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙H ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒy†=‚s‚i‚nƒx–(–)†+ƒcxO űDI3SLś ҤźččCompObjËÍ˙˙˙˙I \ObjInfo˙˙˙˙Î˙˙˙˙K Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙L d_914661951ĂŰŃŔF°ćV@’˜Ă°ćV@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙N PIC ĐÓ˙˙˙˙O LMETA ˙˙˙˙˙˙˙˙˙˙˙˙Q ŹCompObjŇÔ˙˙˙˙\ fś Ň R ˙˙˙.1  `  &˙˙˙˙Ŕ˙˙˙¤˙˙˙`  & MathTypeĐ ú"-TpTŹű@ţTimes New Roman0- 2 Ŕ23ŕ 2 ž2ŕű@ţSymbol-đ 2 Ŕ\=ö 2 ŔÁ+öű@ţTimes New Roman0-đ 2 Ŕśsin(Ž}ŕ“ 2 ŔÁ)“ű@ţSymbol-đ 2 Źtpöű@ţTimes New Roman0-đ 2 Ŕ C+ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ4čqJ0mJLrJ ˆ3†=‚s‚i‚n‚(„pObjInfo˙˙˙˙Ő˙˙˙˙^ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙_ P_1014542623˙˙˙˙˙˙˙˙Ř ŔF°ćV@’˜Ă°ćV@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙a ˆ2‚)†+ƒCţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒy†=‚s‚i‚nƒx–(–)†+ˆ2dO űDI3SCompObj×Ů˙˙˙˙b \ObjInfo˙˙˙˙Ú˙˙˙˙d Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙e d_914662318˙˙˙˙˙˙˙˙ÝŔF°ćV@’˜Ă°ćV@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙g PIC Üß˙˙˙˙h LMETA ˙˙˙˙˙˙˙˙˙˙˙˙j ,CompObjŢŕ˙˙˙˙w fL Ň< źčč Ň ’ ˙˙˙.1  ``&˙˙˙˙Ŕ˙˙˙¤˙˙˙  & MathTypeĐ ú"-T@Tű@ţTimes New Roman- 2 ŹRdyŕÄ 2 RdxŕÄ 2 ŔxÄ 2 Ŕ¤xÄű@ţSymbol-đ 2 ŔŠ=ö 2 Ŕ@ ×pű@ţTimes New Roman-đ 2 ŔäcosÄ஠2 ŔÝ(“ 2 ŔZ )“ 2 Ŕő sin(Ž}ŕ“ 2 Ŕ})“ű ˙Times New Roman˛-đ 2 ÷=3pű@ţTimes New Roman-đ 2 Ŕ~2ŕ 2 ŔĄ 2ŕ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ\čqJ0mJLrJ ƒdƒyƒdƒx†=‚c‚o‚s ˆ3 ‚(ˆ2ƒx‚)†×‚s‚i‚n‚(ˆ2ƒx‚)LńŇ$źččńŇ Ż ˙˙˙.ObjInfo˙˙˙˙á˙˙˙˙y Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙z x_914662439–‘äŔF°ćV@’˜ĂPmX@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙| PIC ăć˙˙˙˙} LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ hCompObjĺç˙˙˙˙ fObjInfo˙˙˙˙č˙˙˙˙  ‚ ƒ „ … † ‡ ˆ ‰ Š ‹ Œ ţ˙˙˙Ž ţ˙˙˙ţ˙˙˙‘ ’ ţ˙˙˙ţ˙˙˙• ţ˙˙˙— ˜ ™ š › œ  ž Ÿ   ţ˙˙˙˘ ţ˙˙˙ţ˙˙˙Ľ ţ˙˙˙ţ˙˙˙¨ ţ˙˙˙Ş Ť Ź ­ Ž Ż ° ą ˛ ł ´ ľ ţ˙˙˙ˇ ţ˙˙˙ţ˙˙˙ş ţ˙˙˙ţ˙˙˙˝ ţ˙˙˙ż Ŕ Á Â Ă Ä Ĺ Ć Ç ţ˙˙˙É ţ˙˙˙ţ˙˙˙Ě ţ˙˙˙ţ˙˙˙Ď ţ˙˙˙Ń Ň Ó Ô Ő Ö × Ř Ů Ú ţ˙˙˙Ü ţ˙˙˙ţ˙˙˙ß ţ˙˙˙ţ˙˙˙â ţ˙˙˙ä ĺ ć ç č é ę ë ě ţ˙˙˙î ţ˙˙˙ţ˙˙˙ń ţ˙˙˙ţ˙˙˙ô ţ˙˙˙ö ÷ ř ů ú ű ü ý ţ ˙ ţ˙˙˙1  ` &˙˙˙˙Ŕ˙˙˙¤˙˙˙` & MathTypeĐ ú"-T@T$T3T7ű@ţTimes New Roman- 2 ŹYdyŕÄ 2 Rduŕŕ 2 Ŕquŕ 2 Ŕduŕ 2 ŔúxÄű@ţSymbol-đ 2 Ŕ˜=ö 2 Ŕü-ö 2 ŔŞ=öű@ţTimes New Roman-đ 2 ŹL1ŕ 2 E2ŕ 2 Ŕ÷2ŕű ˙Times New RomanY-đ 2 ÷l3pű@ţTimes New Roman-đ2 Ŕ÷ where pppBŕēÄpp 2 Ŕcos(Äஓ 2 ŔÓ)“ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙ ˜_914662642˙˙˙˙˙˙˙˙ëŔFPmX@’˜ĂPmX@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙“ PIC ęí˙˙˙˙” LŐ|čqJ0mJLrJ ƒdƒyƒdƒu†=†-ˆ1ˆ2ƒu ˆ3    where  ƒu†=‚c‚o‚s‚(ˆ2ƒx‚)L) ŇTźčč) Ň ? ˙˙˙.1  ` &˙˙˙˙Ŕ˙˙˙¤˙˙˙ŕ META ˙˙˙˙˙˙˙˙˙˙˙˙– ˆCompObjěî˙˙˙˙Ą fObjInfo˙˙˙˙ď˙˙˙˙Ł Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙¤ T & MathTypeĐ ú"-T/Tű@ţTimes New Romanh- 2 Ŕ\yÄ 2 ŔQuŕ 2 Ŕ´C+ű@ţSymbol-đ 2 Ŕ”=ö 2 Ŕř-ö 2 ŔY+öű@ţTimes New Romanh-đ 2 Ź:1ŕ 2 38ŕű ˙Times New Roman-đ 2 ÷L4p & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ8čqJ0mJLrJ ƒy†=†-ˆ1ˆ8ƒu ˆ4 †+ƒCLŇ$ źčč_914662694é÷ňŔFPmX@’˜ĂPmX@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙Ś PIC ńô˙˙˙˙§ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙Š Ň ƒ ˙˙˙.1  ` &˙˙˙˙Ŕ˙˙˙¤˙˙˙` & MathTypeĐ ú"-T/Tű@ţTimes New Roman- 2 Ŕ\yÄ 2 Ŕü xÄ 2 Ŕ0 C+ű@ţSymbol-đ 2 Ŕ”=ö 2 Ŕř-ö 2 ŔŐ +öű@ţTimes New Roman-đ 2 Ź:1ŕ 2 38ŕ 2 Ŕů2ŕű ˙Times New RomanË-đ 2 ÷Ş4pű@ţTimes New Roman-đ 2 ŔQcosÄ஠2 ŔX(“ 2 ŔŐ )“ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qCompObjóő˙˙˙˙ś fObjInfo˙˙˙˙ö˙˙˙˙¸ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙š h_914664105˙˙˙˙˙˙˙˙ůŔFPmX@’˜ĂPmX@’˜ĂŐLčqJ0mJLrJ ƒy†=†-ˆ1ˆ8‚c‚o‚s ˆ4 ‚(ˆ2ƒx‚)†+ƒCL2 ŇČźčč2 Ň $ ˙˙˙.1  `@ &˙˙˙˙Ŕ˙˙˙¤˙˙˙ Ole ˙˙˙˙˙˙˙˙˙˙˙˙ť PIC řű˙˙˙˙ź LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ž PCompObjúü˙˙˙˙Č f & MathTypeĐ ú"-T@Tű@ţTimes New Roman- 2 ŹRdyŕÄ 2 RdxŕÄ 2 ŔäGB 2 ŔřxÄ 2 Ŕ‰yÄű@ţSymbol-đ 2 ŔŠ=öű@ţTimes New Roman-đ 2 Ŕ;(“ 2 ŔŃ,p 2 Ŕb)“ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ4čqJ0mJLrJ ƒdƒyƒdƒx†=ƒG‚(ƒx‚,ƒy‚)Lg_Ă ččObjInfo˙˙˙˙ý˙˙˙˙Ę Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ë P_914664231đPŔFPmX@’˜ĂđóY@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙Í PIC ˙˙˙˙˙Î LMETA ˙˙˙˙˙˙˙˙˙˙˙˙Đ ˆCompObj˙˙˙˙Ű fObjInfo˙˙˙˙˙˙˙˙Ý g_ @ ˙˙˙.1  ŕ &˙˙˙˙Ŕ˙˙˙¤˙˙˙`„ & MathType ú"-T@TTňTWű@ţTimes New Roman- 2 ŹRdyŕÄ 2 RdxŕÄ 2 Ź gŕ 2 ŹŇxÄ 2 hŕ 2 ÄyÄű@ţSymbol-đ 2 ŔŠ=öű@ţTimes New Roman-đ 2 Ź(“ 2 ŹŤ)“ 2 ů(“ 2 )“ & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐDčqJ0mJLrJ ƒdƒyƒdƒx†=ƒg‚(ƒx‚)ƒh‚(ƒy‚)Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ţ `_914664308˙˙˙˙˙˙˙˙ŔFđóY@’˜ĂđóY@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ŕ PIC  ˙˙˙˙á LL: {€hčč: {  ˙˙˙.1  @ &˙˙˙˙Ŕ˙˙˙Đ˙˙˙Ŕ  & MathType`ű@ţTimes New Roman)- 2 €2hŕ 2 €äyÄ 2 €^dyŕÄ 2 €ěgŕ 2 €žxÄ 2 € dxŕÄű@ţMETA ˙˙˙˙˙˙˙˙˙˙˙˙ă HCompObj ˙˙˙˙í fObjInfo˙˙˙˙ ˙˙˙˙ď Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙đ LTimes New Roman--đ 2 €(“ 2 €˝)“ 2 €á(“ 2 €w )“ű@ţSymbol-đ 2 €v=ö & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ0čqJ0mJLrJ ƒh‚(ƒy‚)ƒdƒy†=ƒg‚(ƒx‚)ƒdƒxLg_Ă ččg_ @ ˙˙˙.1  ŕ &˙˙˙˙Ŕ˙˙˙¤˙˙˙`„ & MathType ú"-T@_932365944ŰĺÎŔFđóY@’˜ĂđóY@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ň PIC  ˙˙˙˙ó LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ő ˆTTňTWű@ţTimes New Roman- 2 ŹRdyŕÄ 2 RdxŕÄ 2 Ź gŕ 2 ŹŇxÄ 2 hŕ 2 ÄyÄű@ţSymbol-đ 2 ŔŠ=öű@ţTimes New Roman-đ 2 Ź(“ 2 ŹŤ)“ 2 ů(“ 2 )“ & ˙˙˙˙űź"Systemn-đCompObj˙˙˙˙ fObjInfo˙˙˙˙˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ l_914671957 ŔFđóY@’˜Ăz[@’˜Ă ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙     ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙     ! " # ţ˙˙˙% ţ˙˙˙ţ˙˙˙( ţ˙˙˙ţ˙˙˙+ ţ˙˙˙ţ˙˙˙. ţ˙˙˙ţ˙˙˙1 ţ˙˙˙ţ˙˙˙4 ţ˙˙˙ţ˙˙˙7 ţ˙˙˙9 : ; < = > ? @ A B C D E F G H I J ţ˙˙˙L ţ˙˙˙ţ˙˙˙O P ţ˙˙˙ţ˙˙˙S ţ˙˙˙ţ˙˙˙V W ţ˙˙˙ţ˙˙˙Z ţ˙˙˙ţ˙˙˙] ţ˙˙˙ţ˙˙˙` ţ˙˙˙ţ˙˙˙c ţ˙˙˙ţ˙˙˙f ţ˙˙˙ţ˙˙˙i ţ˙˙˙ţ˙˙˙l ţ˙˙˙ţ˙˙˙o ţ˙˙˙ţ˙˙˙r ţ˙˙˙ţ˙˙˙u ţ˙˙˙ţ˙˙˙x ţ˙˙˙z { | } ~  € ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qTŘPŹcI´gI ƒdƒyƒdƒx†=ƒg‚(ƒx‚)ƒf‚(ƒy‚)LC ŇôźččOle ˙˙˙˙˙˙˙˙˙˙˙˙ PIC ˙˙˙˙ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ tCompObj˙˙˙˙ fC Ň 6 ˙˙˙.1  ` &˙˙˙˙Ŕ˙˙˙¤˙˙˙ŕ  & MathTypeĐ ú"-TóTÉű@ţTimes New Roman- 2 Ŕ†f} 2 ŔFyÄ 2 ŹdyŕÄ 2 dxŕÄ 2 Ŕłgŕ 2 Ŕe xÄű@ţTimes New Roman)-đ 2 Ŕ{(“ 2 Ŕ)“ 2 Ŕ¨(“ 2 Ŕ> )“ű@ţSymbol-đ 2 Ŕ==ö & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ<čqJ0mJLrJ ƒf‚(ƒy‚)ƒdƒyƒdƒx†=ƒg‚(ƒx‚)ObjInfo˙˙˙˙˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ X_914672018˙˙˙˙+ŔFz[@’˜Ăz[@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ PIC ˙˙˙˙ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ HCompObj˙˙˙˙$ fObjInfo˙˙˙˙ ˙˙˙˙& L¤ {źhčč¤ {  ˙˙˙.1  @` &˙˙˙˙Ŕ˙˙˙Đ˙˙˙  & MathType`ű@ţTimes New Roman-- 2 €†f} 2 €FyÄ 2 €ŔdyŕÄ 2 €Ngŕ 2 € xÄ 2 €z dxŕÄű@ţTimes New Roman…-đ 2 €{(“ 2 €)“ 2 €C(“ 2 €Ů )“ű@ţSymbol-đ 2 €Ř=ö & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ0čqJ0mJLrJ ƒf‚(ƒy‚)ƒdƒy†=ƒg‚(ƒEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙' L_10145433012˙˙˙˙# ŔFz[@’˜Ăz[@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙) CompObj"$˙˙˙˙* \x‚)ƒdƒxţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒGƒx–(–) ObjInfo˙˙˙˙%˙˙˙˙, Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙- D_1014543333<( ŔFz[@’˜Ăz[@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙/ CompObj')˙˙˙˙0 \ObjInfo˙˙˙˙*˙˙˙˙2 Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙3 D_914672171˙˙˙˙˙˙˙˙-ŔFz[@’˜Ă0]@’˜Ăţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒgƒx–(–) LY!ŇčźččOle ˙˙˙˙˙˙˙˙˙˙˙˙5 PIC ,/˙˙˙˙6 LMETA ˙˙˙˙˙˙˙˙˙˙˙˙8 źCompObj.0˙˙˙˙K fY!Ň Y ˙˙˙.1  `@&˙˙˙˙Ŕ˙˙˙¤˙˙˙ & MathTypeĐ ú"-T@TTTîű@ţTimes New Romanř- 2 ŹŚdŕ 2 RdxŕÄ 2 Ŕ F 2 ŔyÄ 2 ŔŠxÄ 2 Ŕ F 2 Ŕ yÄ 2 ŔŸxÄ 2 ŔĐyÄ 2 Ŕ+xÄ 2 Ŕ°f} 2 ŔkyÄ 2 Ź*dyŕÄ 2 *dxŕÄű@ţTimes New Roman!-đ 2 ŔP(“ 2 ŔH(“ 2 Ŕě(“ 2 Ŕ‚)))“““ 2 Ŕ> (“ 2 Ŕâ(“ 2 Ŕx))““ 2 Ŕn(“ 2 Ŕ)“ 2 Ŕ (“ 2 ŔD)“ű ˙Times New Romanř-đ 2 ÷m '% 2 ÷˝'%ű@ţSymbol-đ 2 Ŕ¨ =ö 2 Ŕń×p 2 Ŕ=öű@ţTimes New Romanř-đ 2 Ŕš  pű ˙Times New Roman!-đ 2 ÷ń 8 & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ¤ÔlJPqJ8mJ ƒdƒdƒx‚(ƒF‚(ƒy‚(ƒx‚)‚)‚)†=ƒF ‚Š  ‚(ƒy‚(ƒx‚)‚)†×ƒyObjInfo˙˙˙˙1˙˙˙˙M Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙N Ŕ_1014543150˙˙˙˙˙˙˙˙4 ŔF0]@’˜Ă0]@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙Q  ‚Š ‚(ƒx‚)†=ƒf‚(ƒy‚)ƒdƒyƒdƒxđţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€  ƒfƒy–(–)ƒdƒyƒdƒx–[–]ƒdƒx†=ƒgƒx–(–)–[–]ƒdƒxCompObj35˙˙˙˙R \ObjInfo˙˙˙˙6˙˙˙˙T Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙U ¤_1014548451˙˙˙˙˙˙˙˙9 ŔF0]@’˜Ă0]@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙X CompObj8:˙˙˙˙Y \ObjInfo˙˙˙˙;˙˙˙˙[ Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙\ Dţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒFƒy–(–) ţ˙ ˙˙˙˙ ŔFMathType Equation Equation _10145484867F> ŔF0]@’˜Ă0]@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙^ CompObj=?˙˙˙˙_ \ObjInfo˙˙˙˙@˙˙˙˙a Equationô9˛q€@ ƒx~1€V Ůw ţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙b D_1014548511˙˙˙˙˙˙˙˙C ŔF0]@’˜Ă0]@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙d CompObjBD˙˙˙˙e \ObjInfo˙˙˙˙E˙˙˙˙g Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙h H_1014548525ASH ŔFЇ^@’˜ĂЇ^@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙j D ƒGƒx–(–)  nţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€@ ƒx~1€V Ůw CompObjGI˙˙˙˙k \ObjInfo˙˙˙˙J˙˙˙˙m Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙n D_1014548605˙˙˙˙˙˙˙˙M ŔFЇ^@’˜ĂЇ^@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙p CompObjLN˙˙˙˙q \ObjInfo˙˙˙˙O˙˙˙˙s Ole10Native˙˙˙˙˙˙˙˙˙˙˙˙t dţ˙ ˙˙˙˙ ŔFMathType Equation Equation Equationô9˛q€` ƒFƒy–(–)†=ƒGƒx–(–)†+ƒcDI3SLĘ(Ň źčč_914665194WRŔFЇ^@’˜ĂЇ^@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙v PIC QT˙˙˙˙w LMETA ˙˙˙˙˙˙˙˙˙˙˙˙y ÜĘ(Ň j ˙˙˙.1  `%&˙˙˙˙Ŕ˙˙˙¤˙˙˙Ŕ$ & MathTypeĐ ú"-T@TNű@ţTimes New Roman˛- 2 ŹRdAŕ 2 Šdtŕ} 2 Ŕ*kAÄ 2 Ŕü kÄű@ţSymbol-đ 2 ŔÂ=öű@ţTimes New Roman˛-đ ‚ ƒ „ ţ˙˙˙† ţ˙˙˙ţ˙˙˙‰ Š ‹ ţ˙˙˙ţ˙˙˙Ž ţ˙˙˙ ‘ ’ “ ţ˙˙˙• ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙š ţ˙˙˙œ  ž Ÿ ţ˙˙˙Ą ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙Ś ţ˙˙˙¨ Š Ş Ť ţ˙˙˙­ ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙˛ ţ˙˙˙´ ľ ś ˇ ¸ š ş ť ź ţ˙˙˙ž ţ˙˙˙ţ˙˙˙Á ţ˙˙˙ţ˙˙˙Ä ţ˙˙˙Ć Ç Č É Ę Ë Ě Í Î Ď Đ ţ˙˙˙Ň ţ˙˙˙ţ˙˙˙Ő Ö ţ˙˙˙ţ˙˙˙Ů ţ˙˙˙ţ˙˙˙Ü ţ˙˙˙ţ˙˙˙ß ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙ä ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙é ţ˙˙˙ë ě í î ď đ ń ň ó ţ˙˙˙ő ţ˙˙˙ţ˙˙˙ř ţ˙˙˙ţ˙˙˙ű ţ˙˙˙ý ţ ˙ 2 Ŕ˙ where ppBŕēÄpp2 ŔŔ is the cpp}Žp}ŕÄpÄ2 Ŕ onstant ofŕŕŽ}Äŕ}pŕ“2 Ŕ proportiopŕ“ŕŕŕ“}}ŕ2 Ŕo anlity.Äŕ}}}Ňp & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qCompObjSU˙˙˙˙… fObjInfo˙˙˙˙V˙˙˙˙‡ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ˆ Đ_914665580˙˙˙˙˙˙˙˙YŔFЇ^@’˜Ăp`@’˜ĂŐ´čqJ0mJLrJ ƒdƒAƒdƒt†=ƒkƒA  where  ƒk  is the constant of proportioanlity.L„ĘÜčč„Ę ‰ ˙˙˙.Ole ˙˙˙˙˙˙˙˙˙˙˙˙Œ PIC X[˙˙˙˙ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ CompObjZ\˙˙˙˙” f1   `&˙˙˙˙Ŕ˙˙˙đ˙˙˙  & MathType ű@ţSymbol- 2 `4łö & ˙˙˙˙űź"Systemn-đHţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ čqJ0mJLrJ †łObjInfo˙˙˙˙]˙˙˙˙– Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙— (_914665730ţ`ŔFp`@’˜Ăp`@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙˜ L„ĘÜčč„Ę ‰ ˙˙˙.1   `&˙˙˙˙Ŕ˙˙˙đ˙˙˙  & MathType ű@ţSymbol- 2 `4łö & ˙˙˙˙űź"Systemn-đHPIC _b˙˙˙˙™ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙› CompObjac˙˙˙˙  fObjInfo˙˙˙˙d˙˙˙˙˘ ţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ čqJ0mJLrJ †łL„ĘÜčč„Ę ‰ ˙˙˙.Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ł (_914666535˙˙˙˙˙˙˙˙gŔFp`@’˜Ăp`@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙¤ PIC fi˙˙˙˙Ľ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙§ CompObjhj˙˙˙˙Ź fObjInfo˙˙˙˙k˙˙˙˙Ž Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ż (1   `&˙˙˙˙Ŕ˙˙˙đ˙˙˙  & MathType ű@ţSymbol- 2 `4łö & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ čqJ0mJLrJ †ł_914666650e‰nŔFp`@’˜Ăp`@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙° PIC mp˙˙˙˙ą LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ł LL+ŔĚčč+ " ˙˙˙.1  ŕ&˙˙˙˙Ŕ˙˙˙°˙˙˙Ŕ & MathType ű@ţTimes New Roman  - 2  2lim}}] 2  ń(“ 2  3)“ű ˙Times New Roman-đ 2 €ht>ű@ţTimes New Roman  -đ 2  ŇP 2  ’t}ű ˙Symbol-đ 2 €źŽÝ 2 €ĽĽž & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qCompObjoq˙˙˙˙˝ fObjInfo˙˙˙˙r˙˙˙˙ż Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ŕ P_914671212˙˙˙˙˙˙˙˙uŔF•a@’˜Ă•a@’˜ĂŐ4čqJ0mJLrJ '‚l‚i‚m ƒt†Ž†Ľ ƒP‚(ƒt‚)LąŇ÷źččąŇ t ˙˙˙.1  `Ŕ&˙˙˙˙Ŕ˙˙˙¤˙˙˙€ & MathTypeĐ ú"-T@Ole ˙˙˙˙˙˙˙˙˙˙˙˙ PIC tw˙˙˙˙Ă LMETA ˙˙˙˙˙˙˙˙˙˙˙˙Ĺ đCompObjvx˙˙˙˙Ń fT\T# T‰ ű@ţTimes New Roman5- 2 ŹRdPŕ 2 ‘dtŕ} 2 Ŕ8kPÄ 2 Ź_ P 2 m Lúű@ţSymbol-đ 2 ŔĐ=ö 2 Ŕź-öű@ţTimes New Roman4-đ 2 Ŕ(“ 2 Ŕž )“ 2 Ŕ 1ŕ2 ŔM with k ppB}}ŕppŕp2 Ŕy and L conÄŕŕpppÄŕŕ2 ŔŮstant.Ž}Äŕ}p & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐčqJ0mJLrJ ƒdƒPƒdƒt†=ƒkƒP‚(ˆ1†-ƒPƒL‚)  with  k and L  constant.ObjInfo˙˙˙˙y˙˙˙˙Ó Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ô Ź_938258333ö˙˙˙˙|ÎŔF•a@’˜Ă•a@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙× CompObj{}˙˙˙˙Ř fObjInfo˙˙˙˙~˙˙˙˙Ú Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙Ű h_938258395z„ÎŔF°c@’˜Ă°c@’˜Ăţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚL`hIDcI ƒdƒyƒdƒt†=ˆ2ƒyˆ1†"ƒy–(–)ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qOle ˙˙˙˙˙˙˙˙˙˙˙˙Ý CompObj€‚˙˙˙˙Ţ fObjInfo˙˙˙˙ƒ˙˙˙˙ŕ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙á ,ôÚŕIX~I ƒyţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qôÚŕ‡I$vI ƒt_938258424˙˙˙˙˙˙˙˙†ÎŔF°c@’˜Ă°c@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙â CompObj…‡˙˙˙˙ă fObjInfo˙˙˙˙ˆ˙˙˙˙ĺ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ć ,_914669881˙˙˙˙˙˙˙˙‹ŔF°c@’˜Ă°c@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ç PIC Š˙˙˙˙č LLMŇ$źččMŇ & ˙˙˙.1  ` &˙˙˙˙Ŕ˙˙˙¤˙˙˙` & MathTypeĐ ú"-T@Tű@ţTimes New Roman˛- 2 ŹRdyŕÄ 2 RdxŕÄ 2 ŔőyÄű@ţSymbol-đ 2 ŔŠ=öű@ţMETA ˙˙˙˙˙˙˙˙˙˙˙˙ę TCompObjŒŽ˙˙˙˙ô fObjInfo˙˙˙˙˙˙˙˙ö Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙÷ PTimes New Roman˛-đ 2 Ŕä2ŕű ˙Times New Roman-đ 2 ÷â2p & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ4čqJ0mJLrJ ƒdƒyƒdƒx†=ˆ2ƒy ˆ2LqŇ8źččqŇ   ˙˙˙.1  `Ŕ&˙˙˙˙Ŕ˙˙˙¤˙˙˙€ & MathTypeĐ ú"-T@Tű@ţTimes New Roman- 2 ŹR_914670122lž’ŔF°c@’˜Ă°c@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ů PIC ‘”˙˙˙˙ú LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ü $ý˙˙˙Ł„…†ˆ‡Š‰Œ‹Ž‘’“”•—–˜™š›œžŸ Ą¤˘Ľţ˙˙˙§Ś¨ŞŠŤŹ­ŽŻÚŔą˛ł´ľśˇţ˙˙˙šşťź˝žżţ˙˙˙ŮÂĂÄĹĆÇČţ˙˙˙ĘËĚÍÎĎĐţ˙˙˙ŇÓÔŐÖ×Řţ˙˙˙ă°ÜÝŢßŕáâţ˙˙˙ąĺćçčéęëţ˙˙˙íîďđńňóţ˙˙˙ý˙˙˙ö÷řůúűüýţ˙    ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙           ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙ţ˙˙˙ ţ˙˙˙" # $ % & ' ( ) * + ţ˙˙˙- ţ˙˙˙ţ˙˙˙0 ţ˙˙˙ţ˙˙˙3 ţ˙˙˙5 6 7 8 9 : ; < ţ˙˙˙> ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙C ţ˙˙˙E F G H I J K L ţ˙˙˙N ţ˙˙˙ţ˙˙˙Q ţ˙˙˙ţ˙˙˙T ţ˙˙˙ţ˙˙˙W ţ˙˙˙ţ˙˙˙Z ţ˙˙˙ţ˙˙˙] ^ _ ` a ţ˙˙˙ţ˙˙˙d ţ˙˙˙ţ˙˙˙g ţ˙˙˙ţ˙˙˙j ţ˙˙˙ţ˙˙˙m ţ˙˙˙ţ˙˙˙p ţ˙˙˙ţ˙˙˙s t ţ˙˙˙ţ˙˙˙w ţ˙˙˙ţ˙˙˙z { ţ˙˙˙ţ˙˙˙~ ţ˙˙˙ţ˙˙˙dyŕÄ 2 RdxŕÄ 2 ŔxÄ 2 Ŕ˘yÄű@ţSymbol-đ 2 ŔŠ=öű ˙Times New Roman-đ 2 ÷í2p & ˙˙˙˙űź"Systemn-đ  @ÔůIţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qCompObj“•˙˙˙˙ fObjInfo˙˙˙˙–˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ P_914670193˙˙˙˙˙˙˙˙™ŔF°c@’˜ĂP˘d@’˜ĂŐ4čqJ0mJLrJ ƒdƒyƒdƒx†=ƒx ˆ2 ƒyLŚ•4č茕 ^ ˙˙˙.1  @ &˙˙˙˙Ŕ˙˙˙ł˙˙˙ŕó & MathType ú"-ƒOle ˙˙˙˙˙˙˙˙˙˙˙˙ PIC ˜›˙˙˙˙ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙ ÄCompObjšœ˙˙˙˙ fƒ ű@ţTimes New Roman@- 2 2eÄű ˙Times New Romanh­-đ 2 )/xbű`˙Times New Roman@-đ 2 Ť3Pű ˙Times New Romanh­-đ 2 oa3pű@ţTimes New Roman@-đ 2  7ŕű@ţSymbol-đ 2 ą+ö & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ8čqJ0mJLrJ ƒe ƒx ˆ3 ˆ3 †+ˆ7L••ččObjInfo˙˙˙˙˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙ T_914670395—Ź ŔFP˘d@’˜ĂP˘d@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙ PIC Ÿ˘˙˙˙˙ LMETA ˙˙˙˙˙˙˙˙˙˙˙˙! „CompObjĄŁ˙˙˙˙, fObjInfo˙˙˙˙¤˙˙˙˙. •• = ˙˙˙.1  @@&˙˙˙˙Ŕ˙˙˙ł˙˙˙ó & MathType ú"-ƒ˙ƒôű@ţTimes New Romanh- 2 22ŕű`˙Times New Roman-đ 2 ŋ3Pű ˙Times New Romanh-đ 2 oH3pű@ţTimes New Roman-đ 2 eÄű ˙Times New Romanh-đ 2 )xb & ˙˙˙˙űź"Systemn-đ@ţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ4čqJ0mJLrJ ˆ2ƒe ƒx Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙/ P_914670438˙˙˙˙˙˙˙˙§ŔFP˘d@’˜ĂP˘d@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙1 PIC ŚŠ˙˙˙˙2 Lˆ3 ˆ3Lq4ó@ččq4  ˙˙˙.1   &˙˙˙˙Ŕ˙˙˙ą˙˙˙ŕą & MathType ű@ţTimes New Roman  - 2 Ŕ23ŕű ˙Times New RomaMETA ˙˙˙˙˙˙˙˙˙˙˙˙4 CompObj¨Ş˙˙˙˙= fObjInfo˙˙˙˙Ť˙˙˙˙? Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙@ <n-đ 2 ÷Ü2pű@ţTimes New Roman  -đ 2 ŔýeÄű ˙Times New Roman-đ 2 ÷oxb & ˙˙˙˙űź"Systemn-đţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qŐ čqJ0mJLrJ ˆ3ƒe ˆ2ƒxJL<öřĐčč<ö  ˙˙˙.1  €Ŕ&˙˙˙˙Ŕ˙˙˙Ľ˙˙˙€% & MathTypeĐ ú"-t@tű@ţTimes New Roman- 2 Ěn_914670461ĽsŽŔFP˘d@’˜Ăđ(f@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙A PIC ­°˙˙˙˙B LMETA ˙˙˙˙˙˙˙˙˙˙˙˙D @xÄű ˙Times New Roman1-đ 2 [3pű@ţTimes New Roman-đ 2 @Á3ŕ 2 ŕš1ŕű@ţSymbol-đ 2 ŕz+ö & ˙˙˙˙űź"Systemn-đJţ˙ ˙˙˙˙ŔFMicrosoft Equation 2.0 DS Equation Equation.2ô9˛qCompObjŻą˙˙˙˙M fObjInfo˙˙˙˙˛˙˙˙˙O Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙P H_923385951˙˙˙˙˙˙˙˙ľÎŔFđ(f@’˜Ăđ(f@’˜ĂŐ,čqJ0mJLrJ ƒx ˆ3 ˆ3†+ˆ1ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qÖŐ<źfI aI ƒdƒyƒdƒx†=ƒx ˆ3 ƒyOle ˙˙˙˙˙˙˙˙˙˙˙˙R CompObj´ś˙˙˙˙S fObjInfo˙˙˙˙ˇ˙˙˙˙U Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙V X_923386743…ÂşÎŔFđ(f@’˜Ăđ(f@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙X CompObjšť˙˙˙˙Y fObjInfo˙˙˙˙ź˙˙˙˙[ ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qÖŐ4źfI aI ƒdƒyƒdƒx†=ˆ2ƒdƒyƒdƒx†=ƒxƒdƒyƒdƒx†=ƒyƒdƒyƒdƒx†=†"ƒxƒyƒdƒyƒdƒx†=ƒxƒyƒdƒyEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙\ P_923404835˙˙˙˙˙˙˙˙żÎŔFđ(f@’˜Ăđ(f@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙b CompObjžŔ˙˙˙˙c fƒdƒx†=ƒyƒxƒdƒyƒdƒx†=ƒx†+ƒyţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qÖŐTźfI aI ˆ1ƒt ˆ1ƒx †+" ƒdƒt†=‚l‚n‚(ƒx‚)ObjInfo˙˙˙˙Á˙˙˙˙e Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙f p_926427312˝ÇÄÎŔFđ(f@’˜ĂŻg@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙h ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qŰ4`hIDcI ƒdƒyƒdƒx†=ƒx†+ƒyţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS EqCompObjĂĹ˙˙˙˙i fObjInfo˙˙˙˙Ć˙˙˙˙k Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙l P_926427597˙˙˙˙˙˙˙˙ÉÎŔFŻg@’˜ĂŻg@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙n CompObjČĘ˙˙˙˙o fObjInfo˙˙˙˙Ë˙˙˙˙q Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙r „uation Equation.3ô9˛qŰh`hIDcI ƒy†"ˆ1†=ˆ1‚(ƒx†"ˆ0‚)   or   ƒy†=ƒx†+ˆ1ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛q_926427801¸ęÎÎŔFŻg@’˜ĂŻg@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙u CompObjÍĎ˙˙˙˙v fObjInfo˙˙˙˙Đ˙˙˙˙x Űh`hIDcI ƒy†"ˆ2†=ˆ3‚(ƒx†"ˆ1‚)  or   y†=3x-1ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qEquation Native ˙˙˙˙˙˙˙˙˙˙˙˙y „_926427981˙˙˙˙ÖÓÎŔFŻg@’˜ĂŻg@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙| CompObjŇÔ˙˙˙˙} fObjInfo˙˙˙˙Ő˙˙˙˙ Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙€ P_926428209˙˙˙˙˙˙˙˙ŘÎŔFĐźj@’˜ĂĐźj@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙‚  ţ˙˙˙ţ˙˙˙„ ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙‰ ţ˙˙˙ţ˙˙˙ţ˙˙˙ţ˙˙˙Ž ţ˙˙˙ţ˙˙˙‘ ţ˙˙˙ţ˙˙˙” ţ˙˙˙ţ˙˙˙— ţ˙˙˙ţ˙˙˙š ţ˙˙˙ţ˙˙˙ ž Ÿ   Ą ˘ Ł ţ˙˙˙Ľ ţ˙˙˙ţ˙˙˙¨ ţ˙˙˙ţ˙˙˙Ť Ź ­ Ž Ż ° ą ţ˙˙˙ł ´ ľ ś ˇ ¸ š ţ˙˙˙ť ţ˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙Ű4`hIDcI ƒy†"ˆ5†=ˆ7‚(ƒx†"ˆ2‚)ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation Equation.3ô9˛qŰ`hIDcI …”ƒxCompObj×Ů˙˙˙˙ƒ fObjInfo˙˙˙˙Ú˙˙˙˙… Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙† 0_926428249ŃĺÝÎŔF06i@’˜Ă06i@’˜ĂOle ˙˙˙˙˙˙˙˙˙˙˙˙‡ CompObjÜŢ˙˙˙˙ˆ fObjInfo˙˙˙˙ß˙˙˙˙Š Equation Native ˙˙˙˙˙˙˙˙˙˙˙˙‹ 0ţ˙ ˙˙˙˙ÎŔFMicrosoft Equation 3.0 DS Equation 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