$\Large \mathrm{lim}n\Big(\sqrt{(n^2+1)}-\sqrt{(n^2-3)}\Big)$ bằng: $\

$\Large \mathrm{lim}n\Big(\sqrt{(n^2+1)}-\sqrt{(n^2-3)}\Big)$ bằng:

• A. $\Large +\infty$.
• B. 4.
• C. 2.
• D. -1.

$\Large \mathrm{lim}n\Big(\sqrt{(n^2+1)}-\sqrt{(n^2-3)}\Big)$

$\Large =\mathrm{lim}\dfrac{n(n^2+1-n^2+3)}{\sqrt{n^2+1}+\sqrt{n^2-3}}$

$\Large =\mathrm{lim}\dfrac{4n}{\sqrt{n^2+1}+\sqrt{n^2-3}}$

$\Large =\mathrm{lim}\dfrac{4n}{n\sqrt{1+\dfrac{1}{n^2}}+n.\sqrt{1-\dfrac{3}{n^2}}}$

$\Large =\mathrm{lim}\dfrac{4}{\sqrt{1+\dfrac{1}{n^2}}+\sqrt{1-\dfrac{3}{n^2}}}=\dfrac{4}{1+1}=2$.

Chọn đáp án C.