Question

Calcule o limite (x tendendo a zero) de (sen2x)/x:
5
6
4
2
3

Answer 1

Utilizando l'Hôpital

$\lim_{x \to 0}\frac{\sin2x}{x}\\\\ \lim_{x \to 0} 2.\cos2x=2$

Sem utilizar l'Hôpital:

$\lim_{x \to 0}\frac{\sin2x}{x}\\\\ \lim_{x \to 0}\frac{2\sin(x).\cos(x)}{x}\\\\2(\lim_{x \to 0}\frac{\sin(x)}{x}.\lim_{x \to 0}\frac{\cos(x)}{x})\\\\2(1.1)=2$