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).