### Home > APCALC > Chapter 6 > Lesson 6.5.1 > Problem 6-168

6-168.

Determine the exact value of each of the following limits. Note that calculating the exact value requires that the limit be found analytically rather than numerically.

Careful! Be sure to check:

For a limit to exist, the limit from the left must agree with the limit from the right.What does

Recognize that this is Hana's Definition of the Derivative, and find

, or use l'Hôpital's Rule.

, which is also an indeterminate form.

Before using l'Hôpital's Rule, you will need to convert the argument into a single fraction thatTo evaluate this limit, you will have to use l'Hôpital's Rule twice.

To convert this limit into

form, let .

See the hint in part (a).