Home
Class 12
MATHS
Let f be a differentiable function from ...

Let f be a differentiable function from R to R such that `abs(f(x)-f(y))abs(le2)abs(x-y)^(3//2)`,for all `x,y inR`.If `f(0)=1`,then `int_(0)^(1)f^2(x)dx` is equal to

A

0

B

`1/2`

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

IF f(x+f(y))=f(x)+y AA x, y in R and f(0)=1 , then int_(0)^(10)f(10-x)dx is equal to

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . y=f(x) is

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)=1 , then

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

A function f:RtoR is such that f(x+y)=f(x).f(y) for all x.y inR and f(x)ne0 for all x inR . If f'(0)=2 then f'(x) is equal to

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Let f:R to R be a function satisfying f(x+y)=f(x)=lambdaxy+3x^(2)y^(2)"for all "x,y in R If f(3)=4 and f(5)=52, then f'(x) is equal to

If a function f: R ->R be such that f(x-f(y)) = f(f(y) )+xf(y)+f(x) -1 AA x , y in R then f(2)=

Determine all functions f: R->R such that f(x-f(y))=f(f(y))+xf(y)+f(x)-1 AAx , ygeq0 in Rdot