Solved: Binomial seriesa. Find the first four nonzero

Chapter 8, Problem 30E

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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.

\(f(x)=\sqrt{1+x}\);   approximate \(\sqrt{1.06}\).

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.

\(f(x)=\sqrt{1+x}\);   approximate \(\sqrt{1.06}\).

ANSWER:

Solution 30E

Step 1:

(a).We have to find the first four nonzero terms of the taylor series centered at 0 for the function

ie,  we have to find the terms of the maclaurin series for

The maclaurin series of a function

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