Solution: Binomial seriesa. Find the first four nonzero

Chapter 8, Problem 33E

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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 \(1.18^{-2 / 3}\).

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.

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