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  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 ✎

    1. Use the limits above to describe the shape of the graph of . State all horizontal asymptotes, vertical asymptotes and holes.

This limit can be evaluated without any fancy Algebra steps.

Refer to the hint in part (a). Limits like these suggest that the actual value f(−5) and the limit x→−5 agree.

Factor first. Since the denominator → 0, we are investigating whether there is a hole or an asymptote.

This limit →∞.Compare the highest-power term in the numerator and denominator. Does the graph have a horizontal asymptote or does it approach ∞ or −∞?

Refer to the Hints in parts (c) and (d).