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