Home
Class 12
MATHS
Let f: R rarr R be a continuous odd func...

Let `f: R rarr R` be a continuous odd function, which vanishes exactly at one point and `f(1)=1/2`. Suppose that `F(x)=int_(-1)^xf(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 rarr 1)(F(x))/(G(x))=1/(14)`, Then the value of `f(1/2)` is

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is.

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

Let f(x) = int_(-2)^(x)|t + 1|dt , then

If lim_(t rarr x)(x^2f^2(t)-t^2f^2(x))/(t-x)=0 and f(1)=e then solution of f(x)=1 is

f(x)=int_0^x f(t) dt=x+int_x^1 tf(t)dt, then the value of f(1) is

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

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in R . If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to

Let f : R to R be a continuously differentiable function such that f(2) = 6 and f'(2) = 1/48 . If int_(6)^(f(x)) 4t^(3) dt = (x-2) g(x) than lim_( x to 2) g(x) is equal to

Let f:[0,1]to R be a continuous function then the maximum value of int_(0)^(1)f(x).x^(2)dx-int_(0)^(1)x.(f(x))^(2)dx for all such function(s) is:

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. If f(x)=cosx-int0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equa...

    Text Solution

    |

  2. If f^(prime)(x)=f(x)+int0^1f(x)dx ,gi v e nf(0)=1, then the value of ...

    Text Solution

    |

  3. STATEMENT 1: int0^pisqrt(1-sin^2x) dx=0 , STATEMENT 2: int0^picosx dx...

    Text Solution

    |

  4. STATEMENT 1: Let m be any integer. Then the value of Im=int0^pi(sin2m ...

    Text Solution

    |

  5. STATEMENT 1: The value of int0^(2pi)cos^(99)x dx is 0 STATEMENT 2: in...

    Text Solution

    |

  6. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  7. Let S be the area of the region enclosed by y-e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  8. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

    Text Solution

    |

  9. Show that int0^pixf(sinx)dx=pi/2int0^pif(sinx)dxdot

    Text Solution

    |

  10. Let f(x) be a non-constant twice differentiable function defined on (-...

    Text Solution

    |

  11. Let f(x)=int2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Th...

    Text Solution

    |

  12. Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx...

    Text Solution

    |

  13. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

    Text Solution

    |

  14. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

    Text Solution

    |

  15. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) ...

    Text Solution

    |

  16. The option(s) with the values of a and L that satisfy the following eq...

    Text Solution

    |

  17. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

    Text Solution

    |

  18. Prove that int0^1tan^(-1)(1/(1-x+x^2))dx=2int0^1tan^(-1)x dx. Hence ...

    Text Solution

    |

  19. Let f(x)=|[secx,cosx,sec^2x+cotxcos ecx],[cos^2x,cos^2x, cosec^2x],[1,...

    Text Solution

    |

  20. If f(x)=inta^x[f(x)]^(-1)dx and inta^1[f(x)]^(-1)dx=sqrt(2), then

    Text Solution

    |