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3) Suppose F(x) is an antiderivative of f(x). Use the graph of the functionf(x) below to...
Problem 5 (7 point) Suppose that f'(x) is continuous and that F(x) is an antiderivative of f(x). You are given the following table of values: r=0 2 = 2 * = 4 x = 6 -2 6 f(x) 6 F(x) 7 2 -4 -3 2 -4 5 3 (a) Evaluate | ((z) – 3)s -3)?f'(x)dx. (b) Evaluate (* 25 r* f" ()dx
Consider the graph of the function g shown below. The domain of g is [0,10], and the graph of g is comprised of two line segments and a quarter circle. 1. The function F is defined on [0,10] . It is an antiderivative of g and satisfies F(7)=0. Sketch a graph of F 2. Use your knowledge of area to compute F(4). Explain your reasoning. 3. Write a formula for F using an appropriate integral of g. 4. The function...
3. Consider the following piecewise function (a) Draw an accurate graph of f(). (b) As always, f(x), has an infinite number of antiderivatives. Consider an antiderivative F(r). Let us assume that F(r) is continuous (we don't usually have to specify this, but you will see in the bonus part of the question why we do in this case). Let us further assume that F(2) 1. Sketch an accurate graph of F(r). MATH 1203 Assignment #7-Integration Methods Due: Thurs., Apr. 4...
that f'(2) is continuous and that F(x) is an antiderivative of f(1). the following table of values: 6 f(x) F() r=0 = 2 r = 4 1 = 6 -2 1 -4 6 2. -3 5 6 -4 2 3 7 (a) Evaluate [u(z) – f(x) – 3)?f'(x)da. b) Evaluate ſz, za f'(x)dx
answering D) only will be enough. thank you! 9. Use the graph of f'(x) given below to answer the following questions: á Sobo -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 (a) What is ſ s'(x) dx? J-6 (b) If f(-1) = 4, what is f(-6)? (c) If f(0) = 7, what is f(4)? (d) If f(-2) = 0, what is f (6)?
3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and w(x)-g(f(x)) Use the graphs to find the indicated derivatives. If the indicated derivative does not exist, write "D.N.E." in the space provided. Be sure to include work that shows how you arrived at your answer. 20 a) u'3) b) v-4) c) wl) 3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and...
2. The graph of a function, f(x), is provided to the right. 2 Use this graph to answer each of the following questions. (a) You are also told that f(x) passes through (1, 0.8). -4-3-2f11 1 2 3 Find the equation of f(x), where you use the smallest degree possible. -2 (You can write your answer in factored form.) [6 pts] -3 -4 -5 -6 -7 -8 -9 (b) Based on the graph, describe the end behaviors of f(x). [2...
el Find the horizontal asymptotes 14. The graph of a rational functionf(x) is shown, together with its vertical and horizontal asymptotes. a. As x → +00, f (x) → ? b. As x-+-oo, f (x) → ? .5 C. As x →-1+, f(x)-? 5 4 3 2 el Find the horizontal asymptotes 14. The graph of a rational functionf(x) is shown, together with its vertical and horizontal asymptotes. a. As x → +00, f (x) → ? b. As x-+-oo,...
a. Show that all derivatives d"f/dx of f(x)e are equal to each other and use this to b. Evaluate the derivatives d" f/da of f(x)with a a constant and use this to write c. Prove that the Taylor series in part (b) for f(x)-ea converges for all . Explain explicitly d. How many terms in the Taylor series for єェwith Zo = 0 does it take to approximate the write down the Taylor series for e" about an arbitrary point...
6. Linear Approximation a. Suppose you have a function f(x), and suppose you know df|3 = −4 dx. What is the equation of the tangent line to y = f(x) at x = 3, if f(3) = 7? And give an estimate of f(2.8). b. The volume of a sphere of radius r is V = 1 3 πr3 . Find dV in terms of dr. Then find dV V in terms of dr r , and use it to...