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1.7-4 Use Taylor's formula (1.32) to find a power series expansion about c = 0 for sin(7x/2). Find an expression for the remainder, and from this estimate the number of terms that would be needed to guarantee six-significant-digit accuracy forsin(7x/2) for all x on the interval [-1,1]. f"(c)(x – c)² (x) = f(c) + f'(c)(x - c) + + ... 2! A)(c)(x – c)" + R,+1(x) + (1.32) n!

1.7-4 Use Taylor's formula (1.32) to find a power series expansion about c = 0 for sin(7x/2). Find an expression for the remainder, and from this estimate the number of terms that would be needed to guarantee six-significant-digit accuracy forsin(7x/2) for all x on the interval [-1,1]. f"(c)(x – c)² (x) = f(c) + f'(c)(x - c) + + ... 2! A)(c)(x – c)" + R,+1(x) + (1.32) n!

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1.7-4 Use Taylor's formula (1.32) to find a power series expansion about C 0 for sin(7x/2). Find an expression for the remainder, and from this estimate the number of terms that would be needed to guarantee six-significant-digit accuracy forsin(x/2) for all x on the interval [-1,1]. f"(c)(x – c)² f(x) = f(c) + f'(c)(x – c) + + .. • 2! A"(c)(x – c)" + R,+1(x) (1.32) n!
Transcribed Image Text:1.7-4 Use Taylor's formula (1.32) to find a power series expansion about C 0 for sin(7x/2). Find an expression for the remainder, and from this estimate the number of terms that would be needed to guarantee six-significant-digit accuracy forsin(x/2) for all x on the interval [-1,1]. f"(c)(x – c)² f(x) = f(c) + f'(c)(x – c) + + .. • 2! A"(c)(x – c)" + R,+1(x) (1.32) n!
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