Answer:
To Prove:
is equal to the sum of its Maclaurin series.
Step-by-step explanation:
If
, then
for all n. If d is any positive number and |x| ≤ d, then
So Taylor's Inequality, with a = 0 and M =
, says that
Notice that the same constant
works for every value of n.
But, since
,
We have 
It follows from the Squeeze Theorem that
and therefore
for all values of x.

By this theorem above,
is equal to the sum of its Maclaurin series, that is,
for all x.