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g'(x) h'(x) (or the one sided limit, as required): 5. In each case, find g'(x) and h'(x), then find limx→a (a) g(x) = cos(x) - 1, h(x) = sin²(x), a = 0. (b) g(x) = e²-2(x − 3) + 1, h(x) = x² + 2x − 8, a = 2. - (c) g(x) = ln(3|x|), h(x) = 1/√/\|x|, a = 0, limit from above (i.e., from the right).

g'(x) h'(x) (or the one sided limit, as required): 5. In each case, find g'(x) and h'(x), then find limx→a (a) g(x) = cos(x) - 1, h(x) = sin²(x), a = 0. (b) g(x) = e²-2(x − 3) + 1, h(x) = x² + 2x − 8, a = 2. - (c) g(x) = ln(3|x|), h(x) = 1/√/\|x|, a = 0, limit from above (i.e., from the right).

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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Question
5. In each case, find \( g'(x) \) and \( h'(x) \), then find \(\lim_{x \to a} \frac{g'(x)}{h'(x)}\) (or the one-sided limit, as required): (a) \( g(x) = \cos(x) - 1, \hspace{0.2cm} h(x) = \sin^2(x), \hspace{0.2cm} a = 0. \) (b) \( g(x) = e^{x^2}(x - 3) + 1, \hspace{0.2cm} h(x) = x^2 + 2x - 8, \hspace{0.2cm} a = 2. \) (c) \( g(x) = \ln(3|x|), \hspace{0.2cm} h(x) = \frac{1}{\sqrt{|x|}}, \hspace{0.2cm} a = 0, \) limit from above (i.e., from the right).
Transcribed Image Text:5. In each case, find \( g'(x) \) and \( h'(x) \), then find \(\lim_{x \to a} \frac{g'(x)}{h'(x)}\) (or the one-sided limit, as required): (a) \( g(x) = \cos(x) - 1, \hspace{0.2cm} h(x) = \sin^2(x), \hspace{0.2cm} a = 0. \) (b) \( g(x) = e^{x^2}(x - 3) + 1, \hspace{0.2cm} h(x) = x^2 + 2x - 8, \hspace{0.2cm} a = 2. \) (c) \( g(x) = \ln(3|x|), \hspace{0.2cm} h(x) = \frac{1}{\sqrt{|x|}}, \hspace{0.2cm} a = 0, \) limit from above (i.e., from the right).
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