Question

lim \(\dfrac{\sqrt{x^2-x+3}}{2\left|x\right|1}\)

x-> -∞

Answer 1

\(x\rightarrow-\infty\Rightarrow\left|x\right|=-x\)

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