My teacher just touched on this today. I am trying to figure out some problems. I will show you one, and show how I did it. Could you tell me if I am doing this right? I could be totally off. Thanks in advance.

Find the limit and confirm your answer using the sandwich theorem.

lim as x approaches infinity of (1-cosx)/(x^2)

-1 <= cos x <= 1

2 <= 1-cosx <= 0

(2/x^2) <= (1-cosx)/(x^2) <= 0/(x^2)

0 <= (1-cosx)/(x^2) <= 0

So, the answer is 0.

(Thinking) ???