Home
Class 12
MATHS
A real valued function f(x) is given as ...

A real valued function f(x) is given as `f(x) = {{:(int_(0)^(x) 2{x}dx",",x + {x} in I),(x^(2) - x + (1)/(2)",",(1)/(2) lt x lt (3)/(2) and x ne "1, where" []),(x^(2) - x + (1)/(6)",","otherwise"):}` denotes greatest integer less than or equals to x and {} denotes fractional part function of x. Then,

A

f(x) is continuous and differentiable in `x in [-(1)/(2),(1)/(2)]`

B

f(x) is continuous and differentiable in `x in [-(1)/(2),(1)/(2)]`

C

f(x) is continuous and differentiable in `x in [(1)/(2),(3)/(2)]`

D

f(x) is continuous but not differentiable in `x in (0, 1)`

Text Solution

Verified by Experts

The correct Answer is:
D
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

int_(0)^(15/2)[x-1]dx= where [x] denotes the greatest integer less than or equal to x

Solve (1)/(x)+(1)/([2x])={x}+(1)/(3) where [.] denotes the greatest integers function and {.} denotes fractional part function.

solve (x-2)[x]={x}-1, (where [x]and{x} denote the greatest integer function less than or equal to x and the fractional part function,respectively).

f(x) = [x-1] + {x)^{x}, x in (1,3), then f^-1(x) is- (where [.] denotes greatest integer function and (J denotes fractional part function)

The function f(x)=(tan |pi[x-pi]|)/(1+[x]^(2)) , where [x] denotes the greatest integer less than or equal to x, is

Consider the function f(x) = {x+2} [cos 2x] (where [.] denotes greatest integer function & {.} denotes fractional part function.)

The value of the integral, int_1^3 [x^2-2x–2]dx , where [x] denotes the greatest integer less than or equal to x, is :

The domain of the function f(x)=cos^(-1)[secx] , where [x] denotes the greatest integer less than or equal to x, is

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. A real valued function f(x) is given as f(x) = {{:(int(0)^(x) 2{x}dx",...

    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

    |