I tried them several times and got them wrong. I don't understand the way my prof explains how to do them either.

If you could show step by step, as simple as possible, so that I can understand and be able to do them myself.

$\displaystyle \lim_{x \to 0}\frac{1-cosx}{x³}$ lim does not exist

and

$\displaystyle \lim_{x \to 0}\frac{tanx}{sin8x}$ lim is $\displaystyle \frac{1}{8}$

$\displaystyle \lim_{x \to 0} 7x²\cdot cotx\cdot cscx$ lim is $\displaystyle \frac{7}{11}$

I already have the correct answer - I just don't understand how to get there.