Binomial seriesa. Find the first four nonzero

Chapter 8, Problem 32E

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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.

\(f(x)=(1+x)^{-3}\);   approximate \(1 / 1.331=1 / 1.1^{3}\).

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.

\(f(x)=(1+x)^{-3}\);   approximate \(1 / 1.331=1 / 1.1^{3}\).

ANSWER:

Solution 32EStep 1:Given thatf(x) = (1 + x)3: approximate 1/1.331 = l/l.l3.

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