Be careful! Evaluating this limit as
leads us to trouble:
Recall that is an indeterminate form.
That means we do not know if the limit is finite (because the
's 'cancel out') or infinite (because there is a in the denominator).
We can evaluate an indeterminate limit if that limit happens to be a definition of the derivative.
Sure enough, part (a) is Ana's Definition of the Derivative:
, notice that . So we can rewrite the limit as:
So, we just need to find
at and we have evaluated the limit.
Now evaluate that derivative at
Refer to part (a).