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Home > CALC > Chapter 3 > Lesson 3.3.4 > Problem 3-140

3-140.
  1. Evaluate each limit. If the limit does not exist, say so but also state if y is approaching positive or negative infinity. Homework Help ✎

Evaluate.

As in all limits in which x→∞ or x→−∞, compare only the highest power in the numerator and denominator.

Careful! This one can be deceptive. Just because this is a one-sided limit, does not mean that the limit→∞ or −∞. That will only be the case if there is a zero in the denominator that cannot be cancelled out.

This limit is asking you to determine whether the function approaches its vertical asymptote at x = 2 in a positive or negative direction when looked at from the left.

Choose a value a little to the left of 2 and evaluate. You only need to determine if the limit is positive or negative.

= negative value

Limit does not exist, but y→−∞.