# Approximating Functions with Power Series

Keywords: Small Group Activity, Computer Visualization, Maple, Mathematica, Taylor and Power Series

### Highlights of the activity

1. This computer visualization activity is designed to provide students with an understanding of where a power series approximation is valid.
2. Students use Maple/Mathematica and the algebraic formula for the power series to approximate the function $\sin (\theta)$.
3. The whole class discussion focuses on considering how adding coefficients to the approximation increases the accuracy of the approximation and on where the approximation is valid.

### Reasons to spend class time on the activity

This visualization activity helps students to understand how power series can be used to approximate functions, builds students' intuition for the accuracy of power series approximations, and challenges students to consider the number of terms required before an power series approximation is “accurate”.

### Maple Worksheet

vfpowerapprox.mw (Maple 13)

vfpowerapprox.mws (Maple 11 Classic)

### Mathematica Notebook

Authors: Corinne Manogue

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