무리식 극한 미정계수

$x \rightarrow 1$일 때 분모$\rightarrow 0$이므로 분자$\rightarrow 0$이어야 한다. $\displaystyle \sqrt{2 + a} - \sqrt{4} = 0$ $\therefore a = 2$ (주어진식)$\displaystyle = \lim\limits _{x \rightarrow 1} \frac{\sqrt{2 x + 2} - \sqrt{x + 3}}{x ^{2} - 1}$ $\displaystyle = \lim\limits _{x \rightarrow 1} \frac{x - 1}{( x ^{2} - 1 ) ( \sqrt{2 x + 2} + \sqrt{x + 3} )}$ $\displaystyle = \lim\limits _{x \rightarrow 1} \frac{1}{( x + 1 ) ( \sqrt{2 x + 2} + \sqrt{x + 3} )}$ $\displaystyle = \frac{1}{8}$ $\displaystyle \therefore b = \frac{1}{8}$ $\displaystyle \therefore ab = 2 \times \frac{1}{8} = \frac{1}{4}$