Problem

Establish the validity of the Taylor series Is it practical to use this series...

Establish the validity of the Taylor series

Is it practical to use this series directly to compute arctan(1) if ten decimal places (rounded) of accuracy are required? How many terms of the series would be needed? Will loss of significance occur?

Hint: Start with the series for 1/(1 + x²) and integrate term by term. Note that this procedure is only formal; the convergence of the resulting series can be proved by appealing to certain theorems of advanced calculus.

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Solutions For Problems in Chapter 1.2

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