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Estimating remainders Find the remainder term Rn(x)far the
Chapter 1, Problem 12RE(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.)
\(f(x)=e^{x}\); bound \(R_{3}(x)\) for |x| < 1.
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.)
\(f(x)=e^{x}\); bound \(R_{3}(x)\) for |x| < 1.
ANSWER:Solution 12REStep 1:Given thatf(x) = ex; bound R3 (x) for |x|<1.Step2:To find Find the remainder term Rn(x)far the Taylor series centered at 0 for the following fu