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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) ne 1`, then

A

A) `lim_(xto0+)f'((1)/(x))=1`

B

B) `lim_(xto0+)x f((1)/(x))=2`

C

C) `lim_(xto0+)x^(2)f'(x)=0`

D

D) `|f(x)|le2` for all `x in(0,2)`

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The correct Answer is:
A, D
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