직사각형 대각선 극한

$\displaystyle \overline{\mathrm{AC} \mathit{_{n}}} - \overline{\mathrm{OC} \mathit{_{n}}} = \sqrt{n ^{2} + 48 ^{2}} - n$, $\displaystyle \overline{{ B} _{1} { D} _{n}} = \frac{4 8}{n}$이므로 $\displaystyle \mathrm{\lim\limits} _{n \rightarrow \infty} {} \frac{\overline{{ AC} _{n}} - \overline{{ OC} _{n}}}{\overline{{ B} _{1} { D} _{n}}}$$\displaystyle = \lim\limits _{n \rightarrow \infty} {} \frac{\sqrt{n ^{2} + 48 ^{2}} - n}{\frac{48}{n}}$ $\displaystyle = \lim\limits _{n \rightarrow \infty} {} \frac{( \sqrt{n ^{2} + 48 ^{2}} - n ) ( \sqrt{n ^{2} + 48 ^{2}} + n )}{\frac{48}{n} ( \sqrt{n ^{2} + 48 ^{2}} + n )}$ $\displaystyle = \lim\limits _{n \rightarrow \infty} {} \frac{48 ^{2}}{48 ( \sqrt{1 + \frac{48 ^{2}}{n ^{2}}} + 1 )} = \frac{48}{2} = 24$