9. Which derivative does the limit limh→0(2+h)²2-4Ih(A) f'(2) where f(x) = x²(B) f'(2) where f(x) = 2*(C) f'(2) where f(x) = x(D) f'(0) where f(x) = x² + 4(E) f'(0) where f(x) = (2+ x)² - 4correspond to?

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Answered: 9. Which derivative does the limit lim…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Suppose f(x) is a continuous differentiable function. Some of the values of the function and its derivative are shown below. X -2 3 6 7 -3 f(x) 4 F'(x) 6 0 2 (a) Let g(x) = f($). . Find g'(x). Og'(x) = -(2/2) (²) Og'(x) = ($)F($) Og'(x) = -6f'() Og'(x) = ($) f'( ) Og'(x) = f'( =) Now find g'(3) 2 -2 -5 4 3 = (b) Find the equation of the tangent line to f(x) at x = 1. Use y as the dependent variable. Now approximate f(7) =
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1. For each function given below, calculate the derivative at a point f'(a) using the limit definition. (a) f(x) = 2x2 – 3r f'(0) =? (b) f(x) = /2x + I f'(4) =? 1 (c) f(x)= f'(3) =? x - 2 (d) f(x)= (x – 3)3 f'(4) =? 2. For each function f(x) given below, find the general derivative f' (x) as a new function by using the limit definition. (a) f(x) = V – 4 f'(x) =? (b) f(x)= -r³3 f'(x) =? (c) f(r) = f'(x) =? 3x + 1 1 (d) f(x) = f'(x) =? %3D 3. For each function f(x) given below, find the equation of the tangent line at the indicated point. (a) f(x)= x – r² at (2, –2) (b) f(x) = 1– 3r2 at (0, 1) 1 f(x) = 2r (c) at x = 1 (d) f(x) = x + VI at x = 1 4. Given f(x) = ax² + 2x and f'(1) = 5, solve for a.
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(2) Let f(x) be a function whose second derivative is continuous on [-1, 1]. Then fxf"(x). dx = B) f'(1) + f'(-1)-2f (1) +2f(-1) A) f'(1) + f'(-1)-f(1) + f(-1) C) f"(1) + f"(-1)-f(1) + f(-1) D) f'(1) - f'(-1) + f(1) − f(−1) (3) (csc (3x) dx =

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9. Which derivative does the limit lim h→0 (2+h)²2-4 Ih (A) f'(2) where f(x) = x² (B) f'(2) where f(x) = 2* (C) f'(2) where f(x) = x (D) f'(0) where f(x) = x² + 4 (E) f'(0) where f(x) = (2+ x)² - 4 correspond to?