To show that the Maclaurin series for
Explanation of Solution
Given:
The given Maclaurin series for
Calculation:
To show that the Maclaurin series for
This proof can be completed using the Remainder Estimation Theorem, which states:
where
Note that
Since the
which means that for negative values of t, you let
and for positive values of t you let
Now, you can show that
since, by the Remainder Estimation Theorem you know that
and you know that
both
since factorials grow so much faster than exponentials.
So it is proved that
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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