Answer
1) Verify $0/0$ form.
2) If 1) is verified apply equality
$$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}$$
3) Calculate the limit. If the form is indeterminate again repeat from 1).
Work Step by Step
1) If given
$$\lim_{x\to a}\frac{f(x)}{g(x)}$$ calculate
$$\lim_{x\to a} f(x),\quad \lim_{x\to a}g(x).$$
if they are both equal to $0$ we got $0/0$ indeterminate form.
2) Apply equality
$$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}.$$
3) Calculate
$$\lim_{x\to a}f'(x),\quad \lim_{x\to a}g'(x)$$
if $\lim_{x\to a}f'(x)/\lim_{x\to a}g'(x)$ is determinate then the initial limit is equal to this ratio. If not repeat the procedure from step 1) but on the transformed limit.
