Question

Why does the limit of sinx/x as x approaches infinity equal 0?

Answer 1

For a similar reason that 1/x approaches zero, but you can also use L'Hopital's rule to be more formal about it.

Answer 2

We use the squeeze theorem for this.

We know that \(-1\le sin(x) \le 1\).
We also know that \[\Large \lim_{x \rightarrow \infty} \frac{-1}{x} = 0 \text{ and } \lim_{x \rightarrow \infty} \frac{1}{x} = 0\]

So if these go to \( 0\), and \( sin(x)\) must be between them (between \(0\) and \(0\)), it too must go to \(0\).

Answer 3

Thank you both very much!