무리식 수열 극한

$\displaystyle \lim\limits _{n \rightarrow \infty} {} ( \sqrt{n ^{2} + 4 n + 11} - n )$ $\displaystyle = \lim\limits _{n \rightarrow \infty} {} \frac{( \sqrt{n ^{2} + 4 n + 11} - n ) ( \sqrt{n ^{2} + 4 n + 11} + n )}{\sqrt{n ^{2} + 4 n + 11} + n}$ $\displaystyle = \lim\limits _{n \rightarrow \infty} {} \frac{4 n + 11}{\sqrt{n ^{2} + 4 n + 11} + n}$ $\displaystyle = \lim\limits _{n \rightarrow \infty} {} \frac{4 + \frac{11}{n}}{\sqrt{1 + \frac{4}{n} + \frac{11}{n ^{2}}} + 1}$$= 2$