Thread: Limit approaching infinity question

I'm stuck on a question at the moment.

find the limit as x approaches infinity of [cos(2x) - cos(3x)]/x^2

I'm pretty sure the answer will be 0 but i can't work out how to show to working of it.
Cheers for any help.

Originally Posted by notsogreat

I'm stuck on a question at the moment.

find the limit as x approaches infinity of [cos(2x) - cos(3x)]/x^2

I'm pretty sure the answer will be 0 but i can't work out how to show to working of it.
Cheers for any help.

The absolute value of the numerator is at most two, for all x. Therefore your function is bounded above by 2/x^2 and below by -2/x^2.