그래프로 연속·미분가능

[출제의도] 연속성과 미분가능성의 개념 이해하기 ㄱ. $\displaystyle \frac{g ( 2 )}{f ( 2 )} = 0 , \lim\limits _{x \rightarrow 2} {\frac{g ( x )}{f ( x )} = 0}$ (참) ㄴ. $g ( f ( 1 ) ) = - 1$, $\displaystyle \lim\limits _{x \rightarrow 1} {} g ( f ( x ) ) = - 1$(참) ㄷ. $\displaystyle f ( x ) = \begin{cases} 1 & ( 3 \leq x < 4 ) \\ x - 3 & ( 4 \leq x \leq 5 ) \end{cases}$, $g ( x ) = x - 4 ( 3 \leq x \leq 5 )$ $\displaystyle f ( x ) g ( x ) = \begin{cases} x - 4 & ( 3 \leq x < 4 ) \\ ( x - 3 ) ( x - 4 ) & ( 4 \leq x \leq 5 ) \end{cases}$ $\displaystyle \lim\limits _{x \rightarrow 4 - 0} \frac{f ( x ) g ( x ) - f ( 4 ) g ( 4 )}{x - 4} = 1$ $\displaystyle \lim\limits _{x \rightarrow 4 + 0} {} \frac{f ( x ) g ( x ) - f ( 4 ) g ( 4 )}{x - 4} = 1$ (참)