csat-suneung 2018 Q9

csat-suneung · South-Korea · csat__math-science 3 marks Chain Rule Limit Involving Derivative Definition of Composed Functions

For a function $f ( x )$ differentiable on the set of all real numbers, let the function $g ( x )$ be defined as $$g ( x ) = \frac { f ( x ) } { e ^ { x - 2 } }$$ If $\lim _ { x \rightarrow 2 } \frac { f ( x ) - 3 } { x - 2 } = 5$, what is the value of $g ^ { \prime } ( 2 )$? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

For a function $f ( x )$ differentiable on the set of all real numbers, let the function $g ( x )$ be defined as
$$g ( x ) = \frac { f ( x ) } { e ^ { x - 2 } }$$
If $\lim _ { x \rightarrow 2 } \frac { f ( x ) - 3 } { x - 2 } = 5$, what is the value of $g ^ { \prime } ( 2 )$? [3 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5

Paper Questions

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