무리식 극한 미정계수

$x \rightarrow 1$때 (분모)→0이고 수렴하므로 (분자)→0 $\therefore a + b = 0$ $\therefore b = - a$ …… ㉠ $\displaystyle 2 \sqrt{2} = \lim\limits _{x \rightarrow 1} \frac{\frac{a ( x - 1 )}{{\sqrt{x + 1} - \sqrt{2}} ^{\times {\sqrt{x + 1} + \sqrt{2}}}}}{\sqrt{x + 1} + \sqrt{2}}$ $\displaystyle = \lim\limits _{x \rightarrow 1} \frac{a ( x - 1 ) ( \sqrt{x + 1} + \sqrt{2} )}{( x - 1 )}$ $\displaystyle = \lim\limits _{x \rightarrow 1} a ( \sqrt{x + 1} + \sqrt{2} )$ $\displaystyle = 2 \sqrt{2} a$ $\therefore a = 1$ ㉠에서 $b = - 1$ $\therefore ab = - 1$