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Solution: Remainder terms Find the remainder in the Taylor
Chapter 8, Problem 50E(choose chapter or problem)
Remainder terms Find the remainder in the Taylor series centered at the point a for the following functions. Then show that \(\lim \limits_{n \rightarrow \infty} R_{n}(x)=0\) for all x in the interval of convergence.
\(f(x)=\cos x, a=\pi / 2\)
Questions & Answers
QUESTION:
Remainder terms Find the remainder in the Taylor series centered at the point a for the following functions. Then show that \(\lim \limits_{n \rightarrow \infty} R_{n}(x)=0\) for all x in the interval of convergence.
\(f(x)=\cos x, a=\pi / 2\)
ANSWER:Solution 50E
Step 1:
We need to find the remainder in the taylor series expansion of the function centered at
First we find the Taylor series of as follows
Since the derivatives repeat in a cycle of four, we can write the taylor series as follows:
=
=