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Evaluate the following limits.

  1. This is Ana's Definition of the Derivative.

  1. See the hint in part (a).

  1. For limits to infinity, we can compare the numerator with the denominator. As the numerator approaches infinity, oscillates between and ... not very big. As the denominator approaches infinity, also approaches infinity. So the denominator is MUCH larger than the numerator.

  1. Recall that the number is about . It is larger than and smaller than . Use that to compare the dominant terms of the numerator and denominator.