Find the limit.

Question

lim t+2/t-5
t-->5-

Answer 1

first, we observe what happens when t approaches 5:
lim (t+2)/(t-5) as t->5
7/0 = infinity
which can be (+) or (-) infinity

since it's 5- or to the left of 5, some of the values can be 4.99, 4.999, 4.9999,, if we choose for instance, 4.999,
4.999 - 5 = -0.001 *negative*

thus, the lim (t+2)/(t-5) as t->5- is
(-) infinity