# 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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