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onsider the following function. f (x) = cos (x) , a = 5n = 4,0

onsider the following function. f (x) = cos (x) , a = 5n = 4,0

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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**Consider the following function.** \[ f(x) = \cos(x), \, a = \frac{\pi}{3}, \, n = 4, \, 0 \leq x \leq \frac{2\pi}{3} \] **(a)** Approximate \( f \) by a Taylor polynomial with degree \( n \) at the number \( a \). \[ T_4(x) = \] **(b)** Use Taylor's Inequality to estimate the accuracy of the approximation \( f \approx T_n(x) \) when \( x \) lies in the given interval. (Round the answer to six decimal places.) \[ |R_4(x)| \leq \]
Transcribed Image Text:**Consider the following function.** \[ f(x) = \cos(x), \, a = \frac{\pi}{3}, \, n = 4, \, 0 \leq x \leq \frac{2\pi}{3} \] **(a)** Approximate \( f \) by a Taylor polynomial with degree \( n \) at the number \( a \). \[ T_4(x) = \] **(b)** Use Taylor's Inequality to estimate the accuracy of the approximation \( f \approx T_n(x) \) when \( x \) lies in the given interval. (Round the answer to six decimal places.) \[ |R_4(x)| \leq \]
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