Question

lim 4sen (1/x)+2sen(1/x)
x→∞

Answer 1

$\lim_{x \to \infty} \ 4.sen(\frac{1}{x}) + 2.cos(\frac{1}{x})$

$\lim_{x \to \infty} \ 2.[2.sen(\frac{1}{x}) + cos(\frac{1}{x})]$

$2 . [\lim_{x \to \infty} \ 2.sen(\frac{1}{x}) + cos(\frac{1}{x})]$


Aplicando o limite:

$2 . [2.sen(\frac{1}{\infty}) + cos(\frac{1}{\infty})]$

$2 . [2.sen(0) + cos(0)]$

$2 . [2 . 0 + 1]$

$2 . [1]$ = 2


Portanto:

$\boxed{\bold{\lim_{x \to \infty} \ 4.sen(\frac{1}{x}) + 2.sen(\frac{1}{x}) = 2}}$