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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. This is Ana's definition of the derivative: 

    That means  and .

    Find and then the limit will equal .

    Or you could multiply the numerator and denominator by the conjugate of the numerator.

  1. Evaluate. The denominator will not equal zero so the limit and the actual value agree at .

  1. Rewrite the absolute value as a piecewise function but, since , only consider the piece in which .

  1. Think about what the graph of looks like. What does it look like all the way to the right, as ? How does the affect the graph?