Home
Class 12
MATHS
Let g(x)=int0^x f(t).dt,where f is such ...

Let `g(x)=int_0^x f(t).dt`,where f is such that `1/2<=f(t)<=1` for `t in [0,1]` and `0<=f(t)<=1/2` for `t in [1,2]`.Then g(2) satisfies the inequality

Text Solution

Verified by Experts

The correct Answer is:
`rArr" "g(2) in [(1)/(2), (3)/(2)]`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 2|4 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Let g(x)=int_(0)^(x)f(t)dt where fis the function whose graph is shown.

Let f ( x) = int _ 0 ^ x g (t) dt , where g is a non - zero even function . If f(x + 5 ) = g (x) , then int _ 0 ^ x f (t ) dt equals :

Let f(x)=int_(0)^(1)|x-t|dt, then

Let f(x) = int_(0)^(x)|2t-3|dt , then f is

If _(0)^(x)sin(f(t))dt=(x+2)int_(0)^(x)t sin(f(t))dt, wherex >0 then show that f'(x)cot f(x)+(3)/(1+x)=0

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k The value of g(x+2)-g(x) is equal to (A) g(1) (B) 0 (C) g(2) (D) g(3)

Let G(x)=int e^(x)(int_(0)^(x)f(t)dt+f(x))dx where f(x) is continuous on R. If f(0)=1,G(0)=0 then G(0) equals

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let g(x)=int0^x f(t).dt,where f is such that 1/2<=f(t)<=1 for t in [0,...

    Text Solution

    |

  2. For every pair of continuous functions f,g:[0,1]->R such that max{f(x)...

    Text Solution

    |

  3. Let f:R-> R and g:R-> R be respectively given by f(x) = |x| +1 and g...

    Text Solution

    |

  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

    Text Solution

    |

  5. Q. For every integer n, let an and bn be real numbers. Let function f:...

    Text Solution

    |

  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

    Text Solution

    |

  7. "If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le ...

    Text Solution

    |

  8. For the fucntion f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  9. Let g(x) = ((x -1)^(n))/(log cos^(m)(x-1)),0 lt x lt 2, m and n are in...

    Text Solution

    |

  10. Let f and g be real valued functions defined on interval (-1, 1) such ...

    Text Solution

    |

  11. In the following, [x] denotes the greatest integer less than or equal ...

    Text Solution

    |

  12. If f(x)=min.(1,x^2,x^3), then

    Text Solution

    |

  13. Let f(x) = ||x|-1|, then points where, f(x) is not differentiable is/a...

    Text Solution

    |

  14. lff is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, t...

    Text Solution

    |

  15. The domain of the derivative of the function f(x)={t a n^(-1)x ,if|x|l...

    Text Solution

    |

  16. The left hand derivative of f(x)=[x]sin(pix) at x = k, k is an intege...

    Text Solution

    |

  17. Which of the following functions is differentiable at x = 0? cos (|x|...

    Text Solution

    |

  18. For x in R, f(x) = | log 2- sin x| and g(x) = f(f(x)), then

    Text Solution

    |

  19. If the function g(x)={{:(,k sqrt(x+1),0 le x le3),(,mx+2,3lt xle5):...

    Text Solution

    |

  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

    Text Solution

    |