### Home > APCALC > Chapter 3 > Lesson 3.1.1 > Problem 3-18

Evaluate each limit. If the limit does not exist due to a vertical asymptote, then add an approach statement stating if is approaching negative or positive infinity.

Factor the numerator and denominator. If you can cancel out an

, then the limit exists. If not, then it DNE.

You could factor the denominator. Or you could multiply the top and bottom by the conjugate of

.

The

in the denominator will not cancel out. This means that there is a vertical asymptote at . How can you determine if the asymptote approachesor as from the left?Choose a value that is to left of

, and evaluate. Note: You only need to determine if each term is positive or negative. Choose:DNE but

This is a limit

. That means you are looking at end behavior. Is there a horizontal asymptote, or do the-values approachor ? Consider only the terms with the highest power in the numerator and the denominator. Also consider their coefficients, and their signs.