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Let the f (x) be differentiabe function...

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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