Question

Find the limit as x-->-inf

(x+2)^(3/2)+1

----------I know that the answer is infinity but I don't know how to get this answer by hand. Could someone please help me? Thanks a lot!

Answer 1

You can use the (open) sandwich rule.

Since (x+2)^(3/2)+1 > x for all x>1,
so as x->∞, (x+2)^(3/2)+1 -> ∞.