We're supposed to use the Squeeze Theorem to prove that
$\lim_{x\to 0} {1-\cos x\over x^2} = \frac12$
I tried this:
$-1\le \cos x \le 1$ $-1\le -\cos x \le 1$ $0\le 1-\cos x \le 2$ $0\le {1-\cos x\over x^2} \le {2\over x^2}$
Then using limits we have:
$\lim_{x\to 0}0\le \lim_{x\to 0} {1-\cos x\over x^2} \le \lim_{x\to 0}{2\over x^2}$
And for obvious reasons the first limit is $\Bbb {0}$, and the third limit is $\Bbb \infty$
What do I do now? Or what am I doing wrong?
Thanks in advance