\(\lim\limits_{x\rightarrow-\infty}f\left(x\right)=\lim\limits_{x\rightarrow-\infty}\sqrt{2x^2+x}+x\)
\(=\lim\limits_{x\rightarrow-\infty}\dfrac{2x^2+x-x^2}{\sqrt{2x^2+x}-x}\)
\(=\lim\limits_{x\rightarrow-\infty}\dfrac{x^2+x}{\sqrt{x^2\left(2+\dfrac{1}{x}\right)}-x}\)
\(=\lim\limits_{x\rightarrow-\infty}\dfrac{x\left(x+1\right)}{-x\cdot\sqrt{2+\dfrac{1}{x}}-x}\)
\(=\lim\limits_{x\rightarrow-\infty}\dfrac{-x-1}{\sqrt{2+\dfrac{1}{x}}+1}\)
\(=\lim\limits_{x\rightarrow-\infty}\dfrac{x\left(-1-\dfrac{1}{x}\right)}{\sqrt{2+\dfrac{1}{x}}+1}\)
=\(+\infty\) vì \(\left\{{}\begin{matrix}\lim\limits_{x\rightarrow-\infty}\dfrac{-1-\dfrac{1}{x}}{\sqrt{2+\dfrac{1}{x}}+1}=\dfrac{-1}{\sqrt{2}+1}< 0\\\lim\limits_{x\rightarrow-\infty}x=-\infty\end{matrix}\right.\)
