무리식 극한 상수 결정

ⅰ) $\displaystyle \lim\limits _{x \rightarrow - 1} ( \text{분모} ) = 0$이므로 $\displaystyle \lim\limits _{x \rightarrow - 1} ( \text{분자} ) = 0$이다. $\displaystyle \lim\limits _{x \rightarrow - 1} ( 2 - \sqrt{x + a} ) = 0$ $\displaystyle 2 - \sqrt{- 1 + a} = 0 \therefore a = 5$ ⅱ) $\displaystyle \begin{aligned} \therefore b & = \lim\limits _{x \rightarrow - 1} {} \frac{2 - \sqrt{x + 5}}{x + 1} \end{aligned}$ $\displaystyle = \lim\limits _{x \rightarrow - 1} {} \frac{( 2 - \sqrt{x + 5} ) ( 2 + \sqrt{x + 5} )}{( x + 1 ) ( 2 + \sqrt{x + 5} )}$ $\displaystyle = \lim\limits _{x \rightarrow - 1} {} \frac{- ( x + 1 )}{( x + 1 ) ( 2 + \sqrt{x + 5} )}$ $\displaystyle = \lim\limits _{x \rightarrow - 1} {} \frac{- 1}{2 + \sqrt{x + 5}} = - \frac{1}{4}$ $\displaystyle \therefore \frac{a - b}{b} = \frac{5 + \frac{1}{4}}{- \frac{1}{4}} = - 21$