Evaluate the following limit if it exists or show that it does not exist.

Question

Evaluate the following limit if it exists or show that it does not exist.

lim (t² − 4) / (t³ − 8)

t→2

Answer 1

note that (t²-4)/(t³-8) can be re-arranged to be (t+2)(t-2)/(t-2)(t²+2t+4) allowing that to be changed into (t+2)/(t2+2t+4). The lim of that is (2+2)/(4+4+4)= 1/3