Question

lim ( \(\sqrt{5+x^2}-\sqrt{7+x^2}\)) 

x-> -∞

Answer 1

\(=\lim\limits_{x\rightarrow-\infty}\dfrac{5+x^2-7-x^2}{\sqrt{5+x^2}+\sqrt{7+x^2}}=\lim\limits_{x\rightarrow-\infty}\dfrac{-\dfrac{2}{x}}{-\sqrt{\dfrac{5}{x^2}+\dfrac{x^2}{x^2}}-\sqrt{\dfrac{7}{x^2}+\dfrac{x^2}{x^2}}}=0\)