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Trigonometry
Question

Estimating Pi About how many terms of the Taylor ...

Estimating Pi About how many terms of the Taylor series for \(\tan ^ { - 1 } x\) would you have to use to evaluate each term on the right- hand side of the equation \(\pi = 48 \tan ^ { - 1 } \frac { 1 } { 18 } + 32 \tan ^ { - 1 } \frac { 1 } { 57 } - 20 \tan ^ { - 1 } \frac { 1 } { 239 }\)

Answer

\(\left. \begin{array} { l } { \text { (a) } x + \frac { x ^ { 3 } } { 6 } + \frac { 3 x ^ { 3 } } { 40 } + \frac { 5 x ^ { 7 } } { 112 } \text { , radius of convergence } = 1 } \\ { \text { (b) } \frac { \pi } { 2 } - x - \frac { x ^ { 3 } } { 6 } - \frac { 3 x ^ { 5 } } { 40 } - \frac { 5 x ^ { 7 } } { 112 } } \end{array} \right.\)

Solution
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