무리식 극한 미정계수

$x \rightarrow - 3$ 일 때 (분모)$\rightarrow 0$ 이므로 (분자)$\rightarrow 0$ 이어야 한다. $\displaystyle \lim\limits _{x \rightarrow - 3} ( {\sqrt{x ^{2} - x - 3} + a x} )$ $\displaystyle = \sqrt{( - 3 ) ^{2} - ( - 3 ) - 3} - 3 a$ $= 3 - 3 a = 0$ $\therefore$$a = 1$ $\displaystyle \lim\limits _{x \rightarrow - 3} \frac{\sqrt{x ^{2} - x - 3} + x}{x + 3}$ $\displaystyle = \lim\limits _{x \rightarrow - 3} \frac{( \sqrt{x ^{2} - x - 3} + x ) ( \sqrt{x ^{2} - x - 3} - x )}{( x + 3 ) ( \sqrt{x ^{2} - x - 3} - x )}$ $\displaystyle = \lim\limits _{x \rightarrow - 3} \frac{- ( x + 3 )}{( x + 3 ) ( \sqrt{x ^{2} - x - 3} - x )}$ $\displaystyle = \lim\limits _{x \rightarrow - 3} \frac{- 1}{\sqrt{x ^{2} - x - 3} - x}$ $\displaystyle = \frac{- 1}{\sqrt{( - 3 ) ^{2} - ( - 3 ) - 3} - ( - 3 )} = - \frac{1}{6}$ 즉, $\displaystyle b = - \frac{1}{6}$ 이므로 $\displaystyle a + b = \frac{5}{6}$