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3-51.

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. Homework Help ✎

  1. The denominator does not cancel out. That means that there will be a in the denominator when we evaluate at , so the limit does not exist.

    Graphically, there will be a vertical asymptote at . That is why we are asked to find the limit from the right: we want to know if the graph approaches the asymptote towards or .

    So evaluate a value that is to the right of , and see if you get a positive or negative answer.

    Therefore, from the right, the graph of  approaches the vertical asymptote towards .

  1. Evaluate.

  1. This is a limit . Think end behavior. Compare the highest power on the top and bottom. Be sure to consider their coefficients.

  1.  (Careful!)

    Think: The function is . That is a horizontal line. All -values are .