극한 미정계수

$\displaystyle \lim\limits _{\mathit{x} \rightarrow 3} {\left( x ^{2} - 9 \right)} = 0$이므로 $\displaystyle \lim\limits _{\mathit{x} \rightarrow 3} {\left( 2 x ^{2} + ax + b \right)} = 0$ $18 + 3 a + b = 0$ $b = - 3 \left( a + 6 \right)$ $\displaystyle \lim\limits _{\mathit{x} \rightarrow 3} {\frac{2 x ^{2} + ax - 3 \left( a + 6 \right)}{\left( x + 3 \right) \left( x - 3 \right)}}$$\displaystyle = \lim\limits _{\mathit{x} \rightarrow 3} {\frac{\left( x - 3 \right) \left( 2 x + a + 6 \right)}{\left( x + 3 \right) \left( x - 3 \right)}}$ $\displaystyle = \lim\limits _{x \rightarrow 3} {\frac{2 x + a + 6}{x + 3}}$$\displaystyle = \frac{12 + a}{6} = 3$ $a = 6$, $b = - 36$ 따라서 $a + b = - 30$