Question

What is the limit of `(sin(1-cos x))/(x)` as x approaches 0?

Answer 1

It is `0`.

Explanation:

Two fundamental trigonometric limits are:

`lim_(theta rarr 0) sin theta/theta = 1` and `lim_(theta rarr 0) (1-cos theta)/theta = 0`

This question combines them.

`sin(1-cosx)/x = sin(1-cosx)/(1-cosx) * (1-cosx)/x`

The limit of the first ratio is `1` and the limit of the second is `0`, so the limit of the product is `0`