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and sketch its graph. Label all criti 1 c) f (x) = xe-*

and sketch its graph. Label all criti 1 c) f (x) = xe-*

Calculus: Early Transcendentals
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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Please answer (8c), thanks!
forward or backward? Is it going faster or slowing down? c) When does the mass stop? 8 cm b) v(t) = 8 cos(t), a(t) = -8 sin(t): c) s) = cm, v=7a) v(n) = -8, a(n) = Omoving backward and constant velocity; d) t = ! п 3п 6x²-10 x-x3x²+4x g) lim 7. Find the indicated limits, use +∞ or -∞ when appropriate. Use L'Hospital's rule when needed (be sure to justify why you can use it) x-4 a) lim x4r_16 a) 1/8 b) 3√2 b) lim x Cos x-1 x-0 x h)lim 3 cos t c) 16/5 c) lim x-5 d) i) lim 3x²-14x-5 x2-5x sin 4x x-0 x sin x x→∞ ex j) lim g) 2; h) 0; i) 4 d) lim x→0 2 sec (approximately 1.5 sec, 4.7 sec, 7.8 sec, ...) 8 cm j) 0 moving forward, slowing down and S(T) = 0, 3x²-14x-5 x2−5x k) lim In x e) lim x-0+ ex-1 5√√x-1 x--∞ 10x²-x 1) lim In x X→∞ X k) 0 1) 0 m) ∞ f) lim tanh x x→−8 m) lim e¹x x→0+ 8. Use the strategy discussed in class (first and second derivative tests, critical points, concavity, x- and y-intercepts, asymptotes, etc.) to analyze each given function and sketch its graph. Label all critical and inflection points b) r(x) = x² - 4x³ + 1 c) f (x) = xe-x In x a) f(x) = 9. Solve the following optimization problems. Be sure to identify the constraint equation and the maximizing/minimizi function, determine the domain of the optimizing function, check the second derivative for optimum value, and write t answer in complete sentence including appropriate units a) If 1200cm² of metal is available to make a box with square base and open top, find the dimensions of the box with largest possible volume. Determine the maximum volume.
Transcribed Image Text:forward or backward? Is it going faster or slowing down? c) When does the mass stop? 8 cm b) v(t) = 8 cos(t), a(t) = -8 sin(t): c) s) = cm, v=7a) v(n) = -8, a(n) = Omoving backward and constant velocity; d) t = ! п 3п 6x²-10 x-x3x²+4x g) lim 7. Find the indicated limits, use +∞ or -∞ when appropriate. Use L'Hospital's rule when needed (be sure to justify why you can use it) x-4 a) lim x4r_16 a) 1/8 b) 3√2 b) lim x Cos x-1 x-0 x h)lim 3 cos t c) 16/5 c) lim x-5 d) i) lim 3x²-14x-5 x2-5x sin 4x x-0 x sin x x→∞ ex j) lim g) 2; h) 0; i) 4 d) lim x→0 2 sec (approximately 1.5 sec, 4.7 sec, 7.8 sec, ...) 8 cm j) 0 moving forward, slowing down and S(T) = 0, 3x²-14x-5 x2−5x k) lim In x e) lim x-0+ ex-1 5√√x-1 x--∞ 10x²-x 1) lim In x X→∞ X k) 0 1) 0 m) ∞ f) lim tanh x x→−8 m) lim e¹x x→0+ 8. Use the strategy discussed in class (first and second derivative tests, critical points, concavity, x- and y-intercepts, asymptotes, etc.) to analyze each given function and sketch its graph. Label all critical and inflection points b) r(x) = x² - 4x³ + 1 c) f (x) = xe-x In x a) f(x) = 9. Solve the following optimization problems. Be sure to identify the constraint equation and the maximizing/minimizi function, determine the domain of the optimizing function, check the second derivative for optimum value, and write t answer in complete sentence including appropriate units a) If 1200cm² of metal is available to make a box with square base and open top, find the dimensions of the box with largest possible volume. Determine the maximum volume.
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