Solution Found!
Solved: Estimating remainders Find the remainder term
Chapter 1, Problem 14RE(choose chapter or problem)
Estimating remainders Find the remainder term \(R_{n}(x)\) for the Taylor series centered at 0 for the following functions. Find an upper bound for the magnitude of the remainder on the given interval for the given value of n. (The bound is not unique.)
f(x) = ln (1 – x); bound \(R_{3}(x)\) for |x| < 1/2.
Questions & Answers
QUESTION:
Estimating remainders Find the remainder term \(R_{n}(x)\) for the Taylor series centered at 0 for the following functions. Find an upper bound for the magnitude of the remainder on the given interval for the given value of n. (The bound is not unique.)
f(x) = ln (1 – x); bound \(R_{3}(x)\) for |x| < 1/2.
ANSWER:Solution 14RE
Step 1:
Remainder for taylor series is
where
Using this formula for remainder and taking , we get
where