What is the limit as x goes to infinity of (cos(2x)-cos(3x)) / x^2?
-2 <= cos(2x) - cos(3x) <= 2.
This implies that:
-2/x^2 <= [cos(2x) - cos(3x)]/x^2 <= 2/x^2.
Since -2/x^2 and 2/x^2 --> 0 as x --> infinity, then, by the Squeeze Theorem, [cos(2x) - cos(3x)]/x^2 --> 0 as x --> infinity as it is bounded by -2/x^2 and 2/x^2 and the limits are the same.
is this right??