Remainder terms Find the remainder in the Taylor series centered at the point a for the following functions. Then show that for all x in the interval of convergence.
f(x) = sin a, a = 0
First we find the Taylor series of f(x)=sin a ,at a=0 as follows
f(x)=sin x f(0)=0
f’(x)=cos x f’(0)=1
f’’(x)=-sin x f’’(0)=0
f’’’(x)=-cos x f’’’(0)=-1
f’’’’(x)=sin x f’’’’(0)=0
Since the derivatives repeat in a cycle of four, we can write the Maclaurin series as follows:
With , we have
Since is , we know that for all .
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
The full step-by-step solution to problem: 47E from chapter: 9.3 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: Remainder, Centered, Find, functions, interval. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 47E from 9.3 chapter was answered, more than 269 students have viewed the full step-by-step answer. The answer to “Remainder terms Find the remainder in the Taylor series centered at the point a for the following functions. Then show that for all x in the interval of convergence.f(x) = sin a, a = 0” is broken down into a number of easy to follow steps, and 35 words.