Question

Calcule lim x>0 Tg(3x)\2x

Answer 1

Sabemos que:
$\lim_{ \alpha \to \00} \frac{sen \alpha }{ \alpha }= 1 \\ \\ \lim_{x \to \00} \frac{tg3x}{2x} = \lim_{x \to \00} \frac{sen3x}{cos3x}. \frac{1}{2x}= \lim_{x \to 0} \frac{3x.sen3x}{3x} . \frac{1}{cos3x}. \frac{1}{2x}= \\ \\ \lim_{x \to \00} \frac{3x}{2x} . \frac{sen3x}{3x} . \frac{1}{cos3x}= \frac{3}{2}. \lim_{x \to \00} \frac{sen3x}{3x} . \lim_{x \to \00} \frac{1}{cos3x}= \frac{3}{2} .1. \frac{1}{1} \\ \\ = \frac{3}{2}$