8.3. Series and Power Series

Example 8.3.12 (c): Differentiating and Integrating Power Series

Find the derivative and the integral of the series . Simplify your answer and compare with the previous example. Can you use your results to figure out what function this power series represents?

g(x) =
f(x) =
Then you can verify that:
g(x) = f(x)


g(x) = -f(x) + C

There is a familiar pair of functions that have these properties. Do you remember? To help your memory, here is a plot of the functions:

f(x) = g(x) =
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