(a) Give the second-order Taylor polynomial T, (x) for the function f (x) = x±/2, about a = 4. (b) Use Taylor's Theorem to give the Error Term E, (x) = f (x) – T, (x), as a function of x and some z between 4 and x. (c) Estimate the domain of values x for which the error E, () is less than 0.001. Enter a value p for which |E, (x) |< 0.001 for all 4 < x < 4+p, but |E, (x) |> 0.001 for some a < 4+ 2p. (Hint: replace z by 4 , which gives an upper bound to the error term.) (d) Give an upper bound for the error |E, (6)|.

(a) Give the second-order Taylor polynomial T, (x) for the function f (x) = x±/2, about a = 4. (b) Use Taylor's Theorem to give the Error Term E, (x) = f (x) – T, (x), as a function of x and some z between 4 and x. (c) Estimate the domain of values x for which the error E, () is less than 0.001. Enter a value p for which |E, (x) |< 0.001 for all 4 < x < 4+p, but |E, (x) |> 0.001 for some a < 4+ 2p. (Hint: replace z by 4 , which gives an upper bound to the error term.) (d) Give an upper bound for the error |E, (6)|.

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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