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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. Simply evaluate at .

  2. You can multiply the top and bottom by the conjugate:

    You might have noticed that this is Ana's definition of the derivative:

    Rewrite the given limit as:

    Deconstruct the definition:

    Write the derivative equation:

    Evaluate at :

    Either way, your answer should be .

  3. This is Hana's definition of the derivative.

    Find and .

  4. Refer to the hint in part (a).

  5. Which of the problems above can be interpreted as the definition of the derivative at a point?

    Refer to the previous hints.