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Let the `f (x) ` be differentiabe function on the interval `(0,oo) ` such that `f (1) =1 and lim _(t to x) ((t ^(2) f (x) -x ^(2) f (t))/(t ^(2) -x ^(2))) =1/2 AAx gt 0,` then `f (x)` is:

A

`(1)/(3x) + ( 2x ^2)/( 3)`

B

` -(1)/(3x )+(4x^2)/(3)`

C

`-(1)/(x) + (2)/( x^2)`

D

`(1)/(x)`

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A
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