Đáp án:
Giải thích các bước giải:
$\lim _{x\to \infty }\left(\dfrac{3x-5\sin \left(2x\right)+\cos ^2\left(x\right)}{x^2+2}\right)$
$=\lim _{x\to \infty \:}\left(\dfrac{\dfrac{3}{x}-\dfrac{5\sin \left(2x\right)}{x^2}+\dfrac{\cos ^2\left(x\right)}{x^2}}{1+\frac{2}{x^2}}\right)$
$=\dfrac{\lim _{x\to \infty \:}\left(\dfrac{3}{x}-\dfrac{ 5\sin \left(2x\right)}{x^2}+\dfrac{\cos ^2\left(x\right)}{x^2}\right)}{\lim _{x\to \infty \:}\left(1+\frac{2}{x^2}\right)}$
$=0$
------------------------------------------
$\lim _{x\to \:-\infty \:}\left(\dfrac{\cos \left(5x\right)}{2x}\right)$
$=\dfrac{1}{2}\cdot \lim _{x\to \:-\infty \:}\left(\dfrac{\cos \left(5x\right)}{x}\right)$
`=1/2*0=0`
------------------------------------------
$\lim _{x\to \:0\:}x^2\cos \left(\dfrac{2}{nx}\right)=0$
