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Solution: Binomial seriesa. Find the first four nonzero
Chapter 8, Problem 33E(choose chapter or problem)
Binomial series
a. Find the first four nonzero terms of the Taylor series centered at 0 for the given function.
b. Use the first four terms of the series to approximate the given quantity.
\(f(x)=(1+x)^{-2 / 3}\); approximate \(1.18^{-2 / 3}\).
Questions & Answers
QUESTION:
Binomial series
a. Find the first four nonzero terms of the Taylor series centered at 0 for the given function.
b. Use the first four terms of the series to approximate the given quantity.
\(f(x)=(1+x)^{-2 / 3}\); approximate \(1.18^{-2 / 3}\).
ANSWER:Solution 33EStep 1:Given thatf(x)= (1 + x)2/3 approximate 1.182/3Step2:To finda. Find the first four nonzero terms of the Taylor series centered at 0 for the given function.b. Use the first four terms of the series to approximate the given quantity.