Calculus

We can use the fact that the sine function is bounded by the values -1 and 1. Since sin(2x) is bounded, so is sin²(2x). We can then use the Squeeze Theorem to prove that the limit of (sin²(2x))/x as x approaches infinity is 0. This is because x is an increasing function that approaches infinity whereas sin²(2x) is a bounded function and so stays between -1 and 1. Therefore, we can set up the following Squeeze Theorem statement: -1 ≤ (sin²(2x))/x ≤ 1 As x approaches infinity, the values in the inequality above both tend to 0, thus proving that the limit of (sin²(2x))/x, as x approaches infinity, is 0.