Home
Class 12
MATHS
For a real number y, let [y] denotes the...

For a real number `y`, let `[y]` denotes the greatest integer less than or equal to `y`. Then, the function `f(x) = (tan pi[(x -pi)])/(1+[x]^(2)) ` is

A

discontinuous at some `x`

B

continuous at all x, but the derivative f' (x) does not exist for some x

C

`f'(x)` exists for all x but second derivative `f''(x)` does not exist.

D

`f'(x)` exists for all x.

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise PROBLEM SET (2) (TRUE AND FALSE) |4 Videos

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise PROBLEM SET (2) (FILL IN THE BLANKS) |2 Videos

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise PROBLEM SET (1) (FILL IN THE BLANKS) |7 Videos

  • INVERSE CIRCULAR FUNCTIONS

    ML KHANNA|Exercise Self Assessment Test|25 Videos

  • LINEAR PROGRAMMING

    ML KHANNA|Exercise Self Assessment Test|8 Videos

Similar Questions

Explore conceptually related problems

For a real number y, let [y] denotes the greatest integer less than or equal to y. Then, the function f(x) = (tan pi[(x -pi)])/(1+[2]^(2)) is

Let [x] denote the greatest integer less than or equal to x . Then, int_(1)^(-1)[x]dx=?

Let [x] denote the greatest integer less than or equal to x . Then, int_(0)^(1.5)[x]dx=?

Let [x] denotes the greatest integer less than or equal to x and f(x)= [tan^(2)x] .Then

Let [x] denotes the greatest integer less than or equal to x. If f(x) =[x sin pi x] , then f(x) is

Let f(x)=[x^(2)+1],([x] is the greatest integer less than or equal to x) . Ther

ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. The function f defined as - f(x) = (sin x^(2))//x for x ne 0 and f(0) ...

    Text Solution

    |

  2. If f(x) = {{:(1, x lt 0),(1 + sinx, 0 le x lt pi//2):} Then at x=0, t...

    Text Solution

    |

  3. For a real number y, let [y] denotes the greatest integer less than o...

    Text Solution

    |

  4. If f(x) = x [sqrt(x) - sqrt(x+1)], then

    Text Solution

    |

  5. The function f(x) = {{:(|x-3|, x ge 1),(x^(2)//4-3x//2 + 13//4, x lt 1...

    Text Solution

    |

  6. The value of the derivative of |x-1| + |x-3| at x=2 is:

    Text Solution

    |

  7. Let [ ] denote the greatest integer function and f(x) = [tan^(2)x] The...

    Text Solution

    |

  8. If f(x) = {{:((|x+2|)/(tan^(-1)(x+2)), x ne -2),(2, x =-2):},

    Text Solution

    |

  9. If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt...

    Text Solution

    |

  10. The set of all points, where the function f(x) =x/(1+|x|) is differen...

    Text Solution

    |

  11. The set of points where the function f(x) = x |x| is differentiable i...

    Text Solution

    |

  12. Prove that the function If f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" ...

    Text Solution

    |

  13. The set of allpoints of differentiability of the function f(x) ={{:(x^...

    Text Solution

    |

  14. At the point x = 1, the function: f(x) = {{:(x^(3)-1, 1 lt x lt inft...

    Text Solution

    |

  15. Let f(x) = "min" {1, x^(2), x^(3)}, then:

    Text Solution

    |

  16. The function f(x) is defined as: f(x) =1/3 -x, x ,lt 1/3 =(1/3-x)^...

    Text Solution

    |

  17. If f(x)={{:(,x^(2)sin((1)/(x)),x ne 0),(,0, x=0):}, then

    Text Solution

    |

  18. Let g(x)=xf(x), where f(x)={{:(x^(2)sin.(1)/(x),":",x ne0),(0,":",x=0)...

    Text Solution

    |

  19. Let f(x)={{:(0,x lt 0),(x^(2),xge0):}, then for all values of x

    Text Solution

    |

  20. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

    Text Solution

    |