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6-13.
  1. Evaluate each limit. Homework Help ✎

To find the limit as the function approaches ∞, look at the end behavior of the function.

Find the end behavior by looking at only the highest-power terms in the denominator and numerator.

Because the function's end behavior follows the trend of an x² graph, we know that the limit as the function approaches ∞ is also ∞.

This is ALMOST the same problem as part (a) but, evaluate the limit as x→−∞ instead of ∞.
Note: sometimes there is are different end-behavior limits in each direction.

Refer to part (a). Remember to include 10 as part of the highest power for the numerator!

See part (a).

Note: this means that there is a horizontal asymptote of