Question

\(\lim\limits_{x->-\infty}\sqrt{x^2+x}+\sqrt[3]{x^3+2}\)

Answer 1

\(\lim\limits_{x\rightarrow-\infty}\dfrac{x^2+x-x^2}{\sqrt{x^2+x}-x}+\lim\limits_{x\rightarrow-\infty}\dfrac{x^3+2-x^3}{\sqrt[3]{\left(x^3+2\right)^2}+x\sqrt[3]{x^3+2}+x^2}\)

\(=\lim\limits_{x\rightarrow-\infty}\dfrac{\dfrac{x}{x}}{-\sqrt{\dfrac{x^2}{x^2}+\dfrac{x}{x^2}}-\dfrac{x}{x}}+\lim\limits_{x\rightarrow-\infty}\dfrac{2}{\sqrt[3]{\left(x^3+2\right)^2}+x\sqrt[3]{x^3+2}+x^2}=-\dfrac{1}{2}\)