Activity: Using Technology to Visualize Power Series Approximations

In the Maple worksheet
$\qquad\qquad\qquad\qquad$ Power Series Worksheet
or the Mathematica notebook
$\qquad\qquad\qquad\qquad$ Power Series Notebook
you have the opportunity to explore what it means to approximate a given function, in this case $f(\theta)=\sin\theta$, by looking at the first few terms of its power series. Using the coefficients that you found in § {Finding Power Series Coefficients}, you can plot both the function $\sin\theta$ and its various approximations found by truncating the power series, first after one non-zero term, then after two non-zero terms, etc.

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