Question

Alguém pode me ajudar a calcular?


lim 1 sen (3x)/
x→0 tan (3x)

Answer 1

$\lim_{x \to \ 0} \ \frac{sen(3x)}{tg(3x)}$

$\lim_{x \to \ 0} \ \frac{sen(3x)}{\frac{sen(3x)}{cos(3x)}}$

$\lim_{x \to \ 0} \ sen(3x) . \frac{cos(3x)}{sen(3x)}$

$\lim_{x \to \ 0} \ \not{sen(3x)} . \frac{cos(3x)}{\not{sen(3x)}}$

$\lim_{x \to \ 0} \ cos(3x)$


Aplicando o limite:

cos(3.0)
cos(0) = 1


Portanto:

$\boxed{\bol{\lim_{x \to \ 0} \ \frac{sen(3x)}{tg(3x)} \ = \ 1}}$