### Home > CALC > Chapter 6 > Lesson 6.1.4 > Problem 6-53

6-53.

Evaluate.

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:

Since, notice that. So we can rewrite the limit as:

So, we just need to findatand we have evaluated the limit.

Now evaluate that derivative at:

Refer to part (a).