3. (a) Find the 5th order Taylor polynomial about a = 7 for sin x. (b) Use this Taylor polynomial to approximate sin in terms of powers of 2. 11T (c) The remainder term for a polynomial of order n expanded about x = a is R„(x) = f(n+1)(c). (x – a)n+1 (n + 1)! where c lies between a and x. Write down the remainder term for the polynomial that you have found in part (a). (d) Use the remainder term that you have found in part (c) to show that theTaylor polynomial approximation to sin that you found in part (b) is within 10-6 of the actual value of sin . Use your calculator to verify that the difference between sin and your approximation is, indeed, less than 10-6. 12 : 11T

3. (a) Find the 5th order Taylor polynomial about a = 7 for sin x. (b) Use this Taylor polynomial to approximate sin in terms of powers of 2. 11T (c) The remainder term for a polynomial of order n expanded about x = a is R„(x) = f(n+1)(c). (x – a)n+1 (n + 1)! where c lies between a and x. Write down the remainder term for the polynomial that you have found in part (a). (d) Use the remainder term that you have found in part (c) to show that theTaylor polynomial approximation to sin that you found in part (b) is within 10-6 of the actual value of sin . Use your calculator to verify that the difference between sin and your approximation is, indeed, less than 10-6. 12 : 11T

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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