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11. (a) State the Taylor series at 0 for cos(x). Then using the appropriate shortcut, modify this series to find the Taylor series at 0 for cos(x³). Write out at least the first six terms of the series. (b) Evaluate cos (x°) dx exactly, using the series in part (a). (c) Approximate the value of cos (x) dx using the first five terms in your answer to (b), and find a bound on the amount of error this involves.

11. (a) State the Taylor series at 0 for cos(x). Then using the appropriate shortcut, modify this series to find the Taylor series at 0 for cos(x³). Write out at least the first six terms of the series. (b) Evaluate cos (x°) dx exactly, using the series in part (a). (c) Approximate the value of cos (x) dx using the first five terms in your answer to (b), and find a bound on the amount of error this involves.

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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11. (a) State the Taylor series at 0 for cos(x). Then using the appropriate shortcut, modify this series to find the Taylor series at 0 for cos(x³). Write out at least the first six terms of the series. •1 (b) Evaluate cos (x*) dx exactly, using the series in part (a). (c) Approximate the value of cos (x) dx using the first five terms in your answer to (b), and find a bound on the amount of error this involves.
Transcribed Image Text:11. (a) State the Taylor series at 0 for cos(x). Then using the appropriate shortcut, modify this series to find the Taylor series at 0 for cos(x³). Write out at least the first six terms of the series. •1 (b) Evaluate cos (x*) dx exactly, using the series in part (a). (c) Approximate the value of cos (x) dx using the first five terms in your answer to (b), and find a bound on the amount of error this involves.
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