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Question

Let f(x) be a strictly increasing and differentiable function, then
limx0f(x2)f(x)f(x)f(0), equals

A
2
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B
1
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C
1/2
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D
1
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Solution

The correct option is D 1
limx0f(x2)f(x)f(x)f(0)=limx0f(x2)+f(0)f(0)f(x)x0×x0f(x)f(0)=limx0(x.f(x2)f(0)x20f(x)f(0)x0).x0f(x)f(0)
=(0.f(0)f(0)).1f(0)=1
(provided f(0)0)

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