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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. Evaluate.

  1. As in all limits in which  or , compare only the highest power in the numerator and denominator.

  1. Careful! This one can be deceptive. Just because this is a one-sided limit, does not mean that the limit or . That will only be the case if there is a zero in the denominator that cannot be cancelled out.

  1. This limit is asking you to determine whether the function approaches its vertical asymptote at in a positive or negative direction when looked at from the left.

    Choose a value a little to the left of and evaluate. You only need to determine if the limit is positive or negative.

    negative value

    Limit does not exist, but .