# How do you use the Squeeze Theorem to find #lim (1-cos(x))/x# as x approaches zero?

##### 1 Answer

The usual procedure is to use the squeeze theorem (and some geometry/trigonometry) to prove that

Then use that result together with

So we can use the same geometric arguments to get the same bounds on sinx/x for small positive

And for small positive

Using the trigonomtry referred to above, we can rewrite the midle expression to get

Observe that

and

So, by the squeeze theorem,

For small negative

We can still use the squeeze theorem to get:

Because the left and right limits are both

(This feels very artificial to me. Perhaps because I am more familiar with the common approach mentioned at the beginning of this answer. or perhaps because it is artificial. I don't know.)