Question

\(\lim\limits_{x\rightarrow0}\left(\frac{1}{x}+\frac{1}{x^2}\right)\)

\(\lim\limits_{x\rightarrow+\infty}\frac{\sqrt{\left(-x\right)^2+2}}{x-1}\)

\(\lim\limits_{x\rightarrow-\infty}\frac{|x|+\sqrt{x^2+x}}{x+10}\)

Answer 1

\(\lim\limits_{x\rightarrow0}\left(\frac{x+1}{x^2}\right)=\frac{1}{0}=+\infty\)

\(\lim\limits_{x\rightarrow+\infty}\frac{\sqrt{x^2+2}}{x-1}=\lim\limits_{x\rightarrow+\infty}\frac{\sqrt{1+\frac{2}{x^2}}}{1-\frac{1}{x}}=\frac{1}{1}=1\)

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