무리식 극한 미정계수

[출제의도] 함수의 극한 이해하기 $\displaystyle \lim\limits _{x \rightarrow 9} {\frac{x - a}{\sqrt{x} - 3}} = b$에서 $\displaystyle \lim\limits _{x \rightarrow 9} {\left( \sqrt{x} - 3 \right) = 0}$이므로 $\displaystyle \lim\limits _{x \rightarrow 9} {\left( x - a \right)} = 9 - a = 0$ $\therefore$ $a = 9$ $\displaystyle \lim\limits _{x \rightarrow 9} {\frac{x - 9}{\sqrt{x} - 3}} = \lim\limits _{x \rightarrow 9} {\frac{\left( x - 9 \right) \left( \sqrt{x} + 3 \right)}{\left( \sqrt{x} - 3 \right) \left( \sqrt{x} + 3 \right)}}$ $\displaystyle = \lim\limits _{x \rightarrow 9} {\frac{\left( x - 9 \right) \left( \sqrt{x} + 3 \right)}{x - 9}}$ $\displaystyle = \lim\limits _{x \rightarrow 9} {\left( \sqrt{x} + 3 \right)} = 6 = b$ $\therefore$ $b = 6$ 따라서 $a + b = 15$