Question

Find the limit and confirm using the Sandwich Theorem: lim x->infinity (1 - cosx) / (x^2)

Answer 1

Looked at my graphing calculator, then ate a sandwich.
j/k

Answer 2

I'd start with L'Hopital's rule to find the limit.

Answer 3

With these sandwich theorem (aka squeeze theorem) problems, you just need to take the trig function and work from there as follows.:
-1 <= cos(x) <= 1
-1/x^2 <= cos(x)/x^2 <= 1/x^2

Plugging in infinity into x for the leftmost and rightmost parts of the inequality:

0 <= cos(x)/x^2 <= 0

and we can therefore conclude that the limit as x approaches infinity of cos(x)/x^2 is 0.