\(\lim\limits_{x\rightarrow-\infty}\dfrac{\left|x\right|+\sqrt{x^2+x}}{x+10}\)
\(=\lim\limits_{x\rightarrow-\infty}\dfrac{-x+\sqrt{x^2+x}}{x+10}\)
\(=\lim\limits_{x\rightarrow-\infty}\dfrac{-1+\sqrt{1+\dfrac{1}{x}}}{1+\dfrac{10}{x}}=\dfrac{-1+\sqrt{1}}{1}=\dfrac{-1+1}{1}=0\)