Let f: RvecR be a continuous odd functio...

Let `f: RvecR` be a continuous odd function, which vanishes exactly at one point and `f(1)=1/2dot` Suppose that `F(x)=int_(-1)^xf(t)dtfora l lx in [-1,2]a n dG(x)=int_(-1)^x t|f(f(t))|dtfora l lx in [-1,2]dotIf(lim)_(xvec1)(F(x))/(G(x))=1/(14),` Then the value of `f(1/2)` is

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

LIMITS
ARIHANT MATHS|Exercise Exercise For Session 1|9 Videos
LIMITS
ARIHANT MATHS|Exercise Exercise For Session 2|5 Videos
LIMITS
ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|27 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos
LOGARITHM AND THEIR PROPERTIES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|4 Videos

Similar Questions

Explore conceptually related problems

Let f:R rarr R be a continuous odd function,which vanishes exactly at one point and f(1)=(1)/(2). supposs that F(x)=int_(-1)^(x)f(t)dt for all x in[-1,2] and G(x)=int_(-1)^(x)t|f(f(t))|dt for all x in[-1,2]. If lim_(x rarr1)(F(x))/(G(x)) Then the value of f((1)/(2)) is

If int_(0)^(x)f(t)dt=x+int_(x)^(1)f(t)dt ,then the value of f(1) is

Let f(x)=int_(x^(2))^(x^(3)) for x>1 and g(x)=int_(1)^(x)(2t^(2)-Int)f(t)dt(x<1) then

If f(x)=1+(1)/(x)int_(1)^(x)f(t)dt, then the value of (e^(-1)) is

If F(x)=int_(1)^(x) f(t) dt ,where f(t)=int_(1)^(t^(2))(sqrt(1+u^(4)))/(u) du , then the value of F''(2) equals to

If int_(0)^(x) f(t)dt=x+int_(x)^(1) t f(t) dt , then the value of f(1), is

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

If F(x)=int_(1)^(x)(ln t)/(1+t+t^(2))dt then F(x)=-F((1)/(x))

Let f(x) be a continuous function which takes positive values for xge0 and satisfy int_(0)^(x)f(t)dt=x sqrt(f(x)) with f(1)=1/2 . Then

ARIHANT MATHS-LIMITS-Exercise (Questions Asked In Previous 13 Years Exam)

Let alpha, beta in R such that lim(x ->0) (x^2sin(betax))/(alphax-sin...
Text Solution
|
Let m and n be two positive integers greater than 1.If lim(alpha->0) (...
Text Solution
|
Let f: RvecR be a continuous odd function, which vanishes exactly at o...
Text Solution
|
The largets value of non negative integer for which lim(x->1){(-a x+si...
Text Solution
|
Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i...
Text Solution
|
The lim(xto(pi)/2)(cot x-cosx)/((pi-2x)^(3)) equals
Text Solution
|
Let p=lim(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to
Text Solution
|
lim(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n)is equal to
Text Solution
|
lim(xto0)(sin(picos^(2)x))/(x^(2)) is equal to
Text Solution
|
lim(xto0)((1-cosx)(3+cosx))/(x tan 4x) is equal to
Text Solution
|
If lim(xtooo)((x^(2)+x+1)/(x+1)-ax-b)=4, then
Text Solution
|
let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...
Text Solution
|
If ("lim")(xvec0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,s mftheta in ...
Text Solution
|
For xgt0, lim(xto0) {(sinx)^(1//x)+((1)/(x))^sinx}, is
Text Solution
|
underset(h to 0)lim (f(2h+2+h^(2)))/(f(h-h^(2)+1)-f(1))"given that "f'...
Text Solution
|
lim(x->0) (sin(nx)((a-n)nx – tanx))/x^2= 0, when n is a non-zero posit...
Text Solution
|
The integer n for which lim(x rarr 0) ((cos x-1) ( cos x - e^x))/x^n i...
Text Solution
|
Let f:RtoR be such that f(1)=3 andf'(1)=6. Then lim(xto0)[(f(1+x))/(f(...
Text Solution
|
For x epsilonR, lim(xto oo)((x-3)/(x+2))^(x) is equal to
Text Solution
|