극한의 성질

$f ( x )$가 다항함수이므로 $\displaystyle \lim\limits _{x \rightarrow 2} {( x + 1 ) f ( x )}$ $\displaystyle = \lim\limits _{x \rightarrow 2} {( x + 1 ) \times \lim\limits _{x \rightarrow 2} {f ( x )}}$ $\displaystyle = 3 \times \lim\limits _{x \rightarrow 2} {f ( x )}$$= 6$ 에서 $\displaystyle \lim\limits _{x \rightarrow 2} {f ( x ) = 2}$이고 $f ( 2 ) = 2$ $\displaystyle \lim\limits _{x \rightarrow 2} {\left( x ^{2} + ax - 1 \right) f ( x )}$ $\displaystyle = \lim\limits _{x \rightarrow 2} {\left( x ^{2} + ax - 1 \right) \times \lim\limits _{x \rightarrow 2} {f ( x )}}$ $= ( 2 a + 3 ) \times 2$$= 26$ 에서 $a = 5$ 따라서 $a + f ( 2 ) = 5 + 2 = 7$