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2. Define functions sinh(x) and cosh(x) as follows: sinh(r) = = e-e 2 e² + ex and cosh(): = 2 These functions are called hyperbolic sine and hyperbolic cosine, respectively. (a) Use that e n! for all x to find the Maclaurin series for e-*. n=0 (b) Use the Maclaurin series for e and e to find the Maclaurin the series of sinh(x). d (c) Show that da sinh(2)] = problem. cosh(x) using the definitions provided at the beginning of the (d) Starting with the Maclaurin series you found in part (b), use term-by-term differentiation to find the Maclaurin series of cosh(x).

2. Define functions sinh(x) and cosh(x) as follows: sinh(r) = = e-e 2 e² + ex and cosh(): = 2 These functions are called hyperbolic sine and hyperbolic cosine, respectively. (a) Use that e n! for all x to find the Maclaurin series for e-*. n=0 (b) Use the Maclaurin series for e and e to find the Maclaurin the series of sinh(x). d (c) Show that da sinh(2)] = problem. cosh(x) using the definitions provided at the beginning of the (d) Starting with the Maclaurin series you found in part (b), use term-by-term differentiation to find the Maclaurin series of cosh(x).

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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2. Define functions sinh(x) and cosh(x) as follows: sinh(r) = = e-e 2 e² + ex and cosh(): = 2 These functions are called hyperbolic sine and hyperbolic cosine, respectively. (a) Use that e n! for all x to find the Maclaurin series for e-*. n=0 (b) Use the Maclaurin series for e and e to find the Maclaurin the series of sinh(x). d (c) Show that da sinh(2)] = problem. cosh(x) using the definitions provided at the beginning of the (d) Starting with the Maclaurin series you found in part (b), use term-by-term differentiation to find the Maclaurin series of cosh(x).
Transcribed Image Text:2. Define functions sinh(x) and cosh(x) as follows: sinh(r) = = e-e 2 e² + ex and cosh(): = 2 These functions are called hyperbolic sine and hyperbolic cosine, respectively. (a) Use that e n! for all x to find the Maclaurin series for e-*. n=0 (b) Use the Maclaurin series for e and e to find the Maclaurin the series of sinh(x). d (c) Show that da sinh(2)] = problem. cosh(x) using the definitions provided at the beginning of the (d) Starting with the Maclaurin series you found in part (b), use term-by-term differentiation to find the Maclaurin series of cosh(x).
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