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Evaluate each limit. If the limit does not exist, say so but also state if is approaching positive or negative infinity.

  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 .