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(a) Find the Maclaurin polynomials of orders 2, 3 and 4 for f(x) = cos(x). %3D

(a) Find the Maclaurin polynomials of orders 2, 3 and 4 for f(x) = cos(x). %3D

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(a) Find the Maclaurin polynomials of orders 2, 3 and 4 for f(x) = cos(x). (b) Use the result obtained in part (a) to approximate cos 10° with a quadratic polynomial, p2, and compare this approximation to the result from your calculator or from Google. Remember to convert from degrees to radians before using the Maclaurin polynomial. (c) Use Taylor's Theorem with the Lagrange form of the remainder to show that | cos r – p2(x)| < 4! How does this compare with the accuracy that you found in part (b)? (d) Find the MacLaurin series for f(x) = cos(x) and write it using sigma notation. (e) Differentiate the MacLaurin series for g(x) = sin(x) term by term and confirm that you obtain the MacLaurin series for the derivative of sin(x).
Transcribed Image Text:(a) Find the Maclaurin polynomials of orders 2, 3 and 4 for f(x) = cos(x). (b) Use the result obtained in part (a) to approximate cos 10° with a quadratic polynomial, p2, and compare this approximation to the result from your calculator or from Google. Remember to convert from degrees to radians before using the Maclaurin polynomial. (c) Use Taylor's Theorem with the Lagrange form of the remainder to show that | cos r – p2(x)| < 4! How does this compare with the accuracy that you found in part (b)? (d) Find the MacLaurin series for f(x) = cos(x) and write it using sigma notation. (e) Differentiate the MacLaurin series for g(x) = sin(x) term by term and confirm that you obtain the MacLaurin series for the derivative of sin(x).
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