csat-suneung· South-Korea· csat__math-science4 marks
A polynomial function $f ( x )$ and two natural numbers $m , n$ satisfy $$\begin{array} { l l }
\lim _ { x \rightarrow \infty } \frac { f ( x ) } { x ^ { m } } = 1 , & \lim _ { x \rightarrow \infty } \frac { f ^ { \prime } ( x ) } { x ^ { m - 1 } } = a \\
\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x ^ { n } } = b , & \lim _ { x \rightarrow 0 } \frac { f ^ { \prime } ( x ) } { x ^ { n - 1 } } = 9
\end{array}$$ Which of the following are correct? Select all that apply from . (where $a , b$ are real numbers.) [4 points] ㄱ. $m \geqq n$ ㄴ. $a b \geqq 9$ ㄷ. If $f ( x )$ is a cubic function, then $a m = b n$. (1) ㄱ (2) ㄷ (3) ㄱ, ㄴ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
A polynomial function $f ( x )$ and two natural numbers $m , n$ satisfy
$$\begin{array} { l l }
\lim _ { x \rightarrow \infty } \frac { f ( x ) } { x ^ { m } } = 1 , & \lim _ { x \rightarrow \infty } \frac { f ^ { \prime } ( x ) } { x ^ { m - 1 } } = a \\
\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x ^ { n } } = b , & \lim _ { x \rightarrow 0 } \frac { f ^ { \prime } ( x ) } { x ^ { n - 1 } } = 9
\end{array}$$
Which of the following are correct? Select all that apply from <Remarks>. (where $a , b$ are real numbers.) [4 points]
<Remarks>\\
ㄱ. $m \geqq n$\\
ㄴ. $a b \geqq 9$\\
ㄷ. If $f ( x )$ is a cubic function, then $a m = b n$.\\
(1) ㄱ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ