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Without your calculator, evaluate the following limits.
Compute without a calculator

  1. Notice that this is a right-sided limit because is an endpoint on

    There is no limit from the left of the endpoint; so, consequently, this must be written as a one-sided limit.

  2. This is a limit to infinity. We are looking for end-behavior. Compare the highest-power term in the numerator and the denominator.

    There is a horizontal asymptote of .

  3. This is Ana's Definition of the Derivative:


    So Ana's derivative can be evaluated as:

    The limit is equal to .