ࡱ> 463s@ $bjbj.. "TDD!*%%%8%lV&L*z2&6'''''& ( (CzEzEzEzEzEzEz${RH~iz(''((iz''~zH+H+H+(R''CzH+(CzH+H+s y'& ;mx\i%(u:'zz0zu~)r~ty**~yP(2(H+@( L(X(((iziz** &+"**On the final exam, I will focus on Calculus topics, though you will still need to be able to do algebra in order to solve for critical points, simplify, etc. Since I will write your exam, studying your tests 1 3 is wise! Chapter 1 Sec. 1.1The Cartesian Plane and the Distance Formula (Algebra) Sec. 1.2Graphs of Equations (Algebra) Sec. 1.3Lines in the Plane and Slope (Algebra) 1.4Functions (Algebra) 1.5Limits be able to evaluate limits by direct substitution (when it works), by simplifying first and then substituting, by making a table, or by looking at the graph as needed understand one-sided limits be familiar with the properties of limits (pg 51) as needed 1.6Continuity be able to determine the intervals on which a function is continuous identify whether a discontinuity is removable or not Chapter 2 (sections 2.1 2.2) 2.1Definition of the Derivative be able to find the derivative using the limit definition (one question on the test will require use of the limit definitionshortcuts will earn 0 pts on this question) understand what derivatives tell us be able to write an equation for a tangent line 2.2Rules for Differentiation be able to differentiate using shortcuts practice re-writing functions so that shortcuts can be applied be able to write an equation for a tangent line Formulas you need to know (from test 1 material):  EMBED Equation.3  Chapter 2 (sections 2.3 2.7) 2.3 Rates of Change: velocity and marginals know how to find instantaneous rate of change and average rate of change understand the relationship between position, velocity and acceleration be able to find units of a derivative function 2.4 Product and Quotient Rules know them be able to use them and recognize when to use them 2.5 Chain Rule know it be able to use it and recognize when to use it 2.6 Higher Order Derivatives be able to calculate them (& understand meaning) be comfortable with notation 2.7 Implicit Differentiation be able to find  EMBED Equation.3  implicitly dont forget to use product rule or quotient rule when necessary Chapter 3 (sections 3.1 3.4) 3.1 Increasing/Decreasing Functions be able to find where a function is increasing or decreasing (understand what the first derivative tells us about the original function) know what critical numbers are and how to find them Critical numbers occur when__________________________________________ 3.2 Extrema and the 1st Derivative Test know what extrema are (both relative and absolute) be able to find them using the first derivative test 3.3 Concavity and the 2nd Derivative Test understand what the second derivative tells us about the original function know what concavity is and what inflection points are & how to find them be able to use the second derivative test to find extrema 3.4 Optimization be able to optimize any quantity using either 1st or 2nd derivative test you should be able to write your own function if necessary (see homework & suggested problems for examples) Formulas from test 2 (not given)  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  you should also know things like the Pythagorean theorem, formulas involving rectangles and/or rectangular boxes, etc. Ill provide formulas for circles, spheres, cylinders, cones, etc. if needed. Chapter 3 (sections 3.6 3.8) 3.6 Asymptotes Relationship between asymptotes (both horizontal and vertical) and limits 3.7 Curve Sketching: A Summary This section pulls together continuity, differentiability, extrema, concavity, inflection points, and asymptotes (see page 231 for sections referenced) 3.8 Differentials and Marginal Analysis Compute differentials and use them to approximate error. Formula:  EMBED Equation.3  (recall dx = (x) Chapter 4 (sections 4.14.5) 4.1Exponential Functions (Algebra) 4.2Natural Exponential Functions (Algebra) 4.3Derivatives of Exponential Functions Be able to find derivatives of exponential functions. Formulas to know:  EMBED Equation.3  4.4Logarithmic Functions (Algebra review) properties of logs can make differentiation easier! 4.5Derivatives of Logarithmic Functions Be able to find derivatives of logarithmic functions. Formulas to know:  EMBED Equation.3  4.6Exponential Growth and Decay Review problems from this section. Its mostly algebra review, but there are some questions involving calculus concepts. Chapter 5 (sections 5.15.5) 5.1Antiderivatives and indefinite integrals Know what antiderivatives and indefinite integrals are. Know the notation:  EMBED Equation.3  Basic rules you need to know: (next page)  EMBED Equation.3  **This last one is the simple power rule. Notice that it does not work for n = -1 (section 5.3 tells us how to deal with that). 5.2The general power rule Know and be able to use the general power rule:  EMBED Equation.3  (Again, this does not work for n = -1 see section 5.3). 5.3Exponential and Logarithmic integrals Know and be able to use the rules for exponential integrals:  EMBED Equation.3  Know and be able to use the rules for logarithmic integrals:  EMBED Equation.3  5.4Area and the fundamental theorem of calculus Be able to find area under a given graph. Recall that the area under f(x) between x = a and x = b is given by  EMBED Equation.3  Know that  EMBED Equation.3 , and be able to use this to find definite integrals. 5.5The area of a region bounded by two graphs Be able to find the area between two graphs. You may need to find points of intersection first. Chapter 6 (sections 6.1 and 6.2) 6.1Integration by substitution Be able to integrate by substitution. Be able to solve definite integrals by substitution. 6.2Integration by parts Be able to integrate by parts. I will give you the formula:  EMBED Equation.3  on the cover page of your exam. Remember, if you try integration by parts and it makes your problem worse, try a different choice for u and dv. Chapter 7 (7.1, 7.3 7.5?) coverage will depend on what we are able to finish in class. Well discuss this further on the last day of class (review day). 7.1The Three-Dimensional Coordinate System Finding distance between points in 3-dimensional space Finding midpoint between points in 3-dimensional space Finding equations of spheres 7.3 Functions of Several Variables Evaluating functions of several variables Reading contour maps and associating them with 3D functions 7.4 Partial Derivatives Finding partial derivatives; notation:  EMBED Equation.3 , etc. (see text pg 484) Evaluating partial derivatives (i.e. plugging in a point) Finding second partial derivatives 7.5 Extrema of Functions of Two Variables Critical points of functions of two variables Second-partials test for relative extrema (pg 498) (Note: the First-partials test on pg 495 requires that you visualize the graph of the function in 3 dimensions; the Second-partials test does not require this). 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