Limits at infinity

Question

what is the limit at infinity and negative infinity of this radical:

sqrt(t^2-4)

This is possibly the toughest problem I've encountered when attempting to find limits at infinity because I usually deal with fractions, but I'm not sure what to do here. Please show steps on how to figure this out.

Answer 1

When computing the limit at infinity, it helps to think how the function behaves when t is very large. For very large t, √(t^2 - 4) is like √t^2, or t. So √(t^2 - 4) approaches ∞ as t -> ∞.