극한 미정계수

$\displaystyle \lim\limits _{x \rightarrow 2} {\frac{\sqrt{x + a} - 2}{x - 2}} = b$ 에서 $\displaystyle \sqrt{2 + a} = 2 , a = 2$ $\displaystyle \begin{aligned} \lim\limits _{x \rightarrow 2} {\frac{\sqrt{x + 2} - 2}{x - 2}} \times \frac{\sqrt{x + 2} + 2}{\sqrt{x + 2} + 2} \\ = \lim\limits _{x \rightarrow 2} {\frac{1}{\sqrt{x + 2} + 2} = \frac{1}{4}} = b \end{aligned}$ $10 a + 4 b = 21$