Let f:(0,oo)->R be a differentiable func...

Let `f:(0,oo)->R` be a differentiable function such that `f'(x)=2-f(x)/x` for all `x in (0,oo)` and `f(1)=1`, then

A

`lim _( x to 0^(+))f((1)/(x))=1`

B

`lim_(x to 0^+)xf ((1)/(x))=2`

C

`lim_(x to 0^+)x^2f'(x)=0`

D

`|f(x)le 2| "for all " x in (0,2)`

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The correct Answer is:

A

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