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Question

Let f(x) be a twice differentiable function and f(0)=5, then limx03f(x)4f(3x)+f(9x)x2 is equal to:


A

30

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B

120

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C

40

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D

5

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Solution

The correct option is B

120


=limx03f(x)4f(3x)+f(9x)x2 (00form)=limx03f(x)12f(3x)+9f(9x)2x (00form)=limx03f′′(0)36f′′(0)+81f′′(9x)2=3f′′(0)36f′′(0)+81f′′(0)2=24f"(0)=(24).(5)=120


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