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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. 

  1. Factor the numerator and denominator. If you can cancel out an , then the limit exists. If not, then it DNE.

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

  1. The in the denominator will not cancel out. This means that there is a vertical asymptote at . How can you determine if the asymptote approaches or 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

  1. This is a limit . That means you are looking at end behavior. Is there a horizontal asymptote, or do the -values approach or ?

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