Interactive Real Analysis
- part of 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?
Back
Let
.
Simplify your answer and compare with the previous example. Can you use your
results to figure out what function this power series represents?
Backg(x) =Then you can verify that:
f(x) =
g(x) = f(x) and
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) =