If x 12 then x 9 20 the value of x is 14

    • [PDF File]Lecture 10: Linear Approximation - Nathan Pflueger

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      12 is an overestimate of 3 p 9. 4.If f(x) = p x, then f00(x) = 1 4 x 3=2, which is negative for positive x, so f(x) is concave down for positive x. So L(50) = 7 1 14 is an overestimate of p 50. 5.If f(x) = sinx, then we don’t yet know how to compute f00(x). So we can’t yet conclude anything about whether sinxˇxgives an over or under ...

    • [PDF File]Expected Value The expected value of a random variable ...

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      For any function g, the mean or expected value of g(X) is defined by E(g(X)) = sum g(x k) p(x k). Ex. Roll a fair die. Let X = number of dots on the side that comes up. Calculate E(X2). E(X2) 2= 2sum_{i=1}^{6} i p(i) = 1 p(1) + 2 2 p(2) + 32 p(3) + 42 p(4) + 5 p(5) + 62 p(6) = 1/6*(1+4+9+16+25+36) = 91/6 E(X) is the expected value or 1st moment ...

    • [PDF File]Chapter 5: The Normal Distribution

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      (b) What is the value of c for which there is 80%probability that a metal plate has a thickness within the interval [4.3 – c , 4.3 + c]? (Problem 5.1.11 in textbook) Solution: ≤ P(Z≤ x−4.3 0.12)=0.75 Φ(x−4.3 0.12)=0.75

    • [PDF File]Homework 2 Model Solution - Han-Bom Moon

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      x 1 2S. Furthermore, if x 1 = e, then x = e. Because x 6= e, x 1 6= e and x 1 2S0. We claim that collecting fx;x 1gfor all x 2S0forms pairs for all x 2S0. First of all, this is indeed a pair, because if x = x 1, then x2 = xx 1 = e and x = xe = xx2 = x3 = e. Secondly, obviously each element in S0is in one of such pairs. Next, suppose that fx;x ...

    • [PDF File]Section 8.1 Distributions of Random Variables

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      x is the standard deviation and if you square that value, (x)2, you will get the variance. Also, as mentioned in last class, ¯x is the mean or expected value. 1. The probability distribution of a random variable X is given. x 410 490 530 P(X = x) .2 .5 .3 Find the mean, standard deviation, and variance of X. (Round answers to two decimal places.)

    • [PDF File]PHS WorkRoom -20161011112308

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      18. The total cost of a cab ride can be represented by the function f (x) = 3x + 2.5, where x is the number of miles driven. Graph the function. Use the graph to estimate how much the cab will cost if the cab e is 8 miles. 25 20 15 10 Miles D 91 9 cost 19. 0 Joshua is driving to the store. The average distance d in miles he travels over t minutes

    • [PDF File]The Algebra of Functions - Alamo Colleges District

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      The following example will demonstrate how to evaluate a composition for a given value. Example 6. Find (f B g)(3) and (g B f)(3) if f ( x ) = x + 2 and g ( x ) = 4 – x2. Solution . Step 1. Find (f B g)(x) then evaluate for 3. Since (f B g)(x) = f( g(x) ), then = f(4 – x2) = (4 – x. 2) + 2 = 6 – x. 2. Evaluating for 3 (f B g)(3) = 6 ...

    • [PDF File]3.3 Expected Values

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      x), then the expected value of any function h (X), denoted by ... 12. The Variance of . X. ... 20 Rules of Variance According to the first relation in (3.14), the sd in the new unit is the original sd multiplied by the conversion factor. The second relation says that adding or subtracting a

    • [PDF File]Normal Distributions

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      that the value of Xderived from a single trial of the experiment is between two given values x 1 and x 2 (P(x 1 6 X6 x 2)) is the area under the associated normal curve between x 1 and x 2. For any given value x 1, P(X= x 1) = 0, so P(x 1 6 X6 x 2) = P(x 1

    • [PDF File]Approximating functions by Taylor Polynomials.

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      Chapter 4: Taylor Series 17 same derivative at that point a and also the same second derivative there. We do both at once and define the second degree Taylor Polynomial for f (x) near the point x = a. f (x) ≈ P 2(x) = f (a)+ f (a)(x −a)+ f (a) 2 (x −a)2 Check that P 2(x) has the same first and second derivative that f (x) does at the point x = a. 4.3 Higher Order Taylor Polynomials

    • [PDF File]MCQ’s of CH8 Random Variable and Probability Distributions ...

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      If X is A discrete random variable and f(x) is the probability of X, then the expected value of this random variable is equal to: (a) ∑f(x) (b) ∑[x+f(x)] (c) ∑f(x)+x (d) ∑xf(x) MCQ 7.5 Given E(X) = 5 and E(Y) = -2, then E(X - Y) is: (a) 3 (b) 5 (c) 7 (d) -2 MCQ 7.6 Given x = 2 and f(x) = 0.5.

    • [PDF File]4.1 Extreme Values of Functions

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      80. Even functions If an even function ƒ(x) has a local maximum value at can anything be said about the value of ƒ at Give reasons for your answer. 81. Odd functions If an odd function g(x) has a local minimum value at can anything be said about the value of g at Give reasons for your answer. 82.

    • [PDF File]The Mean Value Theorem - Pennsylvania State University

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      ex. Suppose it took 14 seconds for a thermometer to rise from −19°C to ... values of x, −3 ≤ f ′(x) ≤ 2, then what range of values can f (10) have? Since −3 ≤ f ′(x) ≤ 2 for all x, by the Mean Value Theorem the average rate of change of f on any interval has to be bounded between −3 and 2 as well. Therefore, on the interval ...

    • [PDF File]Answer Key - East Brunswick Public Schools

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      33. Let f be a function that is everywhere differentiable. The value of f' (x) is given for selected values of x in the table below. -10 -5 0 5 10 If f '(x) is always increasing, which statement about f(x) must be true? (A) f(x) has a relative minimum at x = 0. f(x) is concave downwards for all x. has a point of inflection at (0, f (0)).

    • [PDF File]Random Variables and Probability Distributions

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      If x 0, then F(x) 0. If 0 x 3, then If x 3, then Thus the required distribution function is Note that F(x) increases monotonically from 0 to 1 as is required for a distribution function. It should also be noted that F(x) in this case is continuous. F(x) • 0 x 0 x3>27 0 x 3 1 x 3 F(x) 3 3 0 f (u) du 3 x 3 f (u) du 3 3 0 1 9 u2 du 3 x 3 0 du 1 ...

    • [PDF File]Lecture 4 : Calculating Limits using Limit Laws

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      (c) Determine the in nite limit (see note 1 above, say if the limit is 1, 1 or D.N.E.) lim x!2 x+1 (x 2). Polynomial and Rational Functions Please review the relevant parts of Lectures 3, 4 and 7 from the Algebra/Precalculus review

    • [PDF File]RS Aggarwal Solutions for Class 10 Maths Chapter 18 Mean ...

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      Sum of all the frequencies = f1+ 5 + 9 +12 + f2 + 3 + 2 = 40 (given) ⇨ f1+ f2 = 9 …(1) Median is 32.5 lies in 30 – 40, so the median class is 30 – 40 N = 40 N/2 = 20 l = 30, h = 10, f = 12 cf = f1 + 5+9 = f1+14 We know, Median=I+{h×(N2–cf)f} Substitute all the value in the above formula, we get 32.5 = 30 + {10 x (20-f1-14)/12 }

    • [PDF File]fcxsdxtfgfcxdx 7=170

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      The Fundamental Theorem of Calculus: If f is a continuous function on [a,b], then Z b a f(x)dx = F(b)F(a) where F is any antiderivative of f,thatisF0 = f. ... (x)dx 12. Find the average value of the function f on the given interval. f(x)=6x+9x2, [0,5] ... 14. The rate of sales of a certain brand of bicycle by a retailer in thousands of dollars ...

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