Home
Class 12
MATHS
Let [x] be the greatest integer function...

Let [x] be the greatest integer function, then `f(x) = ("sin"(1)/(4)pi [x])/([x])`is

A

Not continuous at any point

B

Continuous at 3/2

C

Discontinuous at 2

D

Differentiable at 4/3

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|25 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 7|9 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Complex Number Exercise 8|2 Videos

  • COORDINATE SYSTEM AND COORDINATES

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

Similar Questions

Explore conceptually related problems

Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) is

If [.] denotes the greatest integer function, then f(x)=[x]+[x+(1)/(2)]

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is

Let [.] represent the greatest integer function and f (x)=[tan^2 x] then :

Let f(x)=cos x and g(x)=[x+1],"where [.] denotes the greatest integer function, Then (gof)' (pi//2) is

Let f(x)=sin x,g(x)=[x+1] and h(x)=gof(x) where [.] the greatest integer function. Then h'((pi)/(2)) is

If [ ] denotes the greatest integer function, lim_(x to(pi)/2)(5 sin [cos x])/([cos x]+2) is

Let f(x) = [x] and [] represents the greatest integer function, then

If f(x)=cos[pi/x] cos(pi/2(x-1)) ; where [x] is the greatest integer function of x ,then f(x) is continuous at :

Let f : R to R is a function defined as f(x) where = {(|x-[x]| ,:[x] "is odd"),(|x - [x + 1]| ,:[x] "is even"):} [.] denotes the greatest integer function, then int_(-2)^(4) dx is equal to

ARIHANT MATHS ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. Number of points where the function f(x)=(x^2-1)|x^2-x-2| + sin(|x|) i...

    Text Solution

    |

  2. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  3. Find dy/dx if 2y-e^x=6

    Text Solution

    |

  4. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  5. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  6. The function f(x) = (x^(2) - 1)|x^(2)-6x + 5|+cos|x| is not differenti...

    Text Solution

    |

  7. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |

  8. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} can be made...

    Text Solution

    |

  9. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

    Text Solution

    |

  10. Consider f(x)=[[2(sinx-sin^3x)+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx...

    Text Solution

    |

  11. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

    Text Solution

    |

  12. Let f(x) = max{|x^2 - 2 |x||,|x|} and g(x) = min{|x^2 - 2|x||, |x|} th...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. Let f(x) be continuous and differentiable function for all reals and f...

    Text Solution

    |

  15. Let [x] be the greatest integer function, then f(x) = ("sin"(1)/(4)pi ...

    Text Solution

    |

  16. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","f...

    Text Solution

    |

  17. If both f(x) & g(x) are differentiable functions at x=x0then the fun...

    Text Solution

    |

  18. Number of points of non-differentiability of the function g(x) = [x^2...

    Text Solution

    |

  19. Find dy/dx if y= xtanx

    Text Solution

    |

  20. If f((x)/(y))=(f(x))/(f(y)) forall x, y in R, y ne 0 and f'(x) exists ...

    Text Solution

    |