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

Evaluate each limit. If the limit does not exist, say so but also state if

*y*is approaching positive or negative infinity. Homework Help ✎

Factor the numerator and denominator. If you can cancel out an (*x*−2), 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 (*x*−2) in the denominator will not cancel out. This means that there is a vertical asymptote at *x* = 2. How can we determine if the asymptote approaches +∞ or −∞ as *x* → 2^{−} from the left?

Choose a value that is to left of *x* = 2, and evaluate. Note: we only need to determine if each term is positive or negative. Choose *x* → 1.9:

*DNE* but *y* → −∞.

This is a limit *x*→∞. That means we are looking at end behavior. Is there a horizontal asymptote, or do the *y*-values approach ∞ or −∞?

Consider only the terms with the highest power in the numerator and the denominator. Also consider their coefficients, and their signs.