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Maclaurin series

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1. Find the maclaurin series for f(x) = e^(3x) using the definition of the Maclaurin series. Assume that f has a power series representation. Find the associated radius of convergence.

2. Find the taylor series for f(x) = sin(x) centered at a = (pi/2), using the definition of a taylor series. Assume that f has a power series representation. Find the associated radius of convergence.

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Solution Preview

1. Find the Maclaurin series for f(x) = e^(3x) using the definition of the Maclaurin series. Assume that f has a power series representation. Find the associated radius of convergence.
Maclaurin Series for any function f(x) is given by
... where ...

Solution Summary

Maclaurin series are conceptualized. The definition for series representation is examined.

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