### Home > CALC > Chapter 2 > Lesson 2.4.1 > Problem 2-142

Determine the values of the following limits. If the limit does not exist, indicate why not.

This is a one-sided limit because the domain of

begins at . Consequently, the limit exists from the right, but not from the left.

Factor first. If you can 'cancel out' the denominator, then the graph has a hole (not a vertical asymptote) and the limit exists.

Evaluate. The denominator will not equal zero. So the limit and the actual value agree.

Visualize the graph of

. Both graphs have the same end behavior (horizontal asymptote).

For limits in which

or, we are looking for end behavior. For example, is there a horizontal asymptote?Since the numerator has a higher power,

, than the denominator,, there is no horizontal asymptote. Thus the limit goes to eitheror . The limit goes to

because:

Refer to hint in part (e).