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Answer: Remainder terms Find the remainder in the Taylor
Chapter 8, Problem 49E(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.
\(f(x)=e^{-x}, a=0\)
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.
\(f(x)=e^{-x}, a=0\)
ANSWER:Solution 49EStep 1:We need to find the remainder in the taylor series expansion of the function centered at First we find the Taylor series of f(x)=sin a ,at a=0 as followsSince the derivatives repeat in a cycle of four, we can write the Maclaurin series as follows: ==