Consider f(x) = arcsin(x) on the interval -≤ x ≤1 Here are the first six derivatives of this function: f'(x) √1-22 f"(x) (1-x2)2 f"" (x): 2x2+1 (1-x2) f(4)(x) = 6x3+9x (1-x2) f(5) (x) = 24x+72x²+9 (1-x²) f(6)(x) = 120x³+600x³+225x (1-2) (a) Write down the fifth degree Taylor Polynomial for this function centered at x = 0 (b) Use your polynomial from (a) to approximate arcsin() (c) Determine the maximum error for approximating arcsin(x) on ½ ≤ x ≤ using the fifth degree Taylor Polynomial. Hint: For (c) it will be helpful to know that |f(6) (x)| is maximized on this interval at x =

Consider f(x) = arcsin(x) on the interval -≤ x ≤1 Here are the first six derivatives of this function: f'(x) √1-22 f"(x) (1-x2)2 f"" (x): 2x2+1 (1-x2) f(4)(x) = 6x3+9x (1-x2) f(5) (x) = 24x+72x²+9 (1-x²) f(6)(x) = 120x³+600x³+225x (1-2) (a) Write down the fifth degree Taylor Polynomial for this function centered at x = 0 (b) Use your polynomial from (a) to approximate arcsin() (c) Determine the maximum error for approximating arcsin(x) on ½ ≤ x ≤ using the fifth degree Taylor Polynomial. Hint: For (c) it will be helpful to know that |f(6) (x)| is maximized on this interval at x =

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...

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