Question

Tìm \(\lim\left(\sqrt{n^2+7}-\sqrt{n^2+5}\right)\).

Answer 1

\(\lim\limits\left(\sqrt{n^2+7}-\sqrt{n^2+5}\right)\)

\(=\lim\limits\dfrac{n^2+7-n^2-5}{\sqrt{n^2+7}+\sqrt{n^2+5}}\)

\(=\lim\limits\dfrac{2}{\sqrt{n^2+7}+\sqrt{n^2+5}}\)

\(=\lim\limits\dfrac{\dfrac{2}{n}}{\sqrt{1+\dfrac{7}{n^2}}+\sqrt{1+\dfrac{5}{n^2}}}=\dfrac{0}{\sqrt{1}+\sqrt{1}}=0\)