csat-suneung 2021 Q17

csat-suneung · South-Korea · csat__math-humanities 4 marks Applied differentiation Finding parameter values from differentiability or equation constraints

Two polynomial functions $f ( x )$ and $g ( x )$ satisfy $$\lim _ { x \rightarrow 0 } \frac { f ( x ) + g ( x ) } { x } = 3 , \quad \lim _ { x \rightarrow 0 } \frac { f ( x ) + 3 } { x g ( x ) } = 2$$ For the function $h ( x ) = f ( x ) g ( x )$, what is the value of $h ^ { \prime } ( 0 )$? [4 points]
(1) 27
(2) 30
(3) 33
(4) 36
(5) 39

Two polynomial functions $f ( x )$ and $g ( x )$ satisfy
$$\lim _ { x \rightarrow 0 } \frac { f ( x ) + g ( x ) } { x } = 3 , \quad \lim _ { x \rightarrow 0 } \frac { f ( x ) + 3 } { x g ( x ) } = 2$$
For the function $h ( x ) = f ( x ) g ( x )$, what is the value of $h ^ { \prime } ( 0 )$? [4 points]\\
(1) 27\\
(2) 30\\
(3) 33\\
(4) 36\\
(5) 39

Paper Questions

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