Let P,(z) be the second-order Taylor polynomial for cos z centered at z = 0. Suppose that P3(z) is used to approximate cos z for |z| < 0.6. The error in this approximation is the absolute value of the difference between the actual value and the approximation. That is, Error = |P2(z) – cos z|. Use the Taylor series remainder estimate to bound the error in the approximation. Your answer should be a number; that is, you should give a bound for the error which works for all z in the given interval. Hint: Notice that the second- and third-order Taylor polynomials are the same. So you could think of your approximation of cos z as a second-order approximation OR a third-order approximation. Which one gives you a better bound?

Let P,(z) be the second-order Taylor polynomial for cos z centered at z = 0. Suppose that P3(z) is used to approximate cos z for |z| < 0.6. The error in this approximation is the absolute value of the difference between the actual value and the approximation. That is, Error = |P2(z) – cos z|. Use the Taylor series remainder estimate to bound the error in the approximation. Your answer should be a number; that is, you should give a bound for the error which works for all z in the given interval. Hint: Notice that the second- and third-order Taylor polynomials are the same. So you could think of your approximation of cos z as a second-order approximation OR a third-order approximation. Which one gives you a better bound?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.3: Change Of Basis

Problem 17EQ

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