Question

giá trị của \(\lim\limits_{x\to -∞} f(x)=\dfrac{\sqrt{x^2-3}}{x+3}\)

Answer 1

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

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

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

\(=\dfrac{-\sqrt{1-0}}{1+0}=-\dfrac{1}{1}=-1\)