lim[x:0,3x(cos7x-1)/(sin7x-7x)] using l'hopital's rule

Question

need the limit using L'hopitals rule.

Answer 1

On substituting we get form, so by L'spital rule.

First apply derivative to the numerator and denominator.

On substituting, again we get form.

Again apply derivative to the numerator and denominator.

On substituting, again we get form.

Again apply derivative to the numerator and denominator.

The solution is