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Let f:(0, oo)rarr(0, oo) be a differenti...

Let `f:(0, oo)rarr(0, oo)` be a differentiable function such that `f(1)=e` and `lim_(trarrx)(t^(2)f^(2)(x)-x^(2)f^(2)(t))/(t-x)=0`. If `f(x)=1`, then x is equal to :

A

2e

B

`(1)/(2)`

C

e

D

`(1)/(2e)`

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