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Let f(x) be differentiable on the interv...

Let `f(x)` be differentiable on the interval `(0,oo)` such that `f(1)=1` and `lim_(t->x) (t^2f(x)-x^2f(t))/(t-x)=1` for each `x>0`. Then `f(x)=`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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