CPM Homework Banner

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.

  1. This is a one-sided limit because the domain of  begins at . Consequently, the limit exists from the right, but not from the left.

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

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

  1. Visualize the graph of . Both graphs have the same end behavior (horizontal asymptote).

  1. 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 either or .

    The limit goes to because:

  1. Refer to hint in part (e).