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 findat and we have evaluated the limit.
Now evaluate that derivative at:
Refer to part (a).