### Home > CALC > Chapter 4 > Lesson 4.4.2 > Problem 4-137

4-137.

Without your calculator, evaluate the following limits.

Notice that this is a right-sided limit because

is an endpoint on

There is no limit from the left of the endpoint; so, consequently, this must be written as a one-sided limit.

This is a limit to infinity. We are looking for end-behavior. Compare the highest-power term in the numerator and the denominator.

There is a horizontal asymptote of.

This is Ana's Definition of the Derivative:

*f*and

So Ana's derivative can be evaluated as:

The limit is equal to.