Home
Class 12
MATHS
Let f(x) =x[1/x]+x[x] if x!=0 ; 0 if x ...

Let `f(x) =x[1/x]+x[x] if x!=0 ; 0 if x =0` where[x] denotes the greatest integer function. then the correct statements are (A) Limit exists for x=-1 (B) f(x) has removable discontinuity at x =1 (C) f(x) has non removable discontinuity at x =2 (D) f(x) is non removable discontinuous at all positive integers

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

If f(x)= [sin^2x] (where [.] denotes the greatest integer function ) then :

Draw the graph of f(x) = [x^(2)], x in [0, 2) , where [*] denotes the greatest integer function.

If f(x)={(x[x], 0lexlt2),((x-1)[x], 2lexle3'):} , where [.] denotes the greatest integer function, then

If f(x)= cos [ pi^(2)] x+ cos[ -pi^(2)] x where [x] denotes the greatest integer function, then show that f(-pi)=0

If f(x)=cos |x|+[|sin x/2|] (where [.] denotes the greatest integer function), then f (x) is

Let f (x)= [x] where [x] denotes the greatest integer contained in x. Which one of the following is correct ?

The function f(x) = [x]^2-[x^2] (where [.] denotes the greatest integer function ) is discontinuous at

draw the graph of f(x)=x+[x] , [.] denotes greatest integer function.

Let f(x)={1+|x|,x<-1 [x],xgeq-1 , where [.] denotes the greatest integer function. The find the value of f{f(-2.3)}dot

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^3). Then find g'(x) i...

    Text Solution

    |

  2. If y=cos^(-1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2))),t h e n(dy)/(dx) i...

    Text Solution

    |

  3. Let f(x) =x[1/x]+x[x] if x!=0 ; 0 if x =0 where[x] denotes the greate...

    Text Solution

    |

  4. Let y=x^(3)-8x+7 and x=f(t)." If "(dy)/(dt)=2 and x=3 at t = 0," then ...

    Text Solution

    |

  5. f is a strictly monotonic differentiable function with f^(prime)(x)=1/...

    Text Solution

    |

  6. Suppose f: R->R^+ be a differentiable function such that 3f(x+y)=f(x)f...

    Text Solution

    |

  7. Vertices of a variable acute angled triangle A B C lies on a fixed cir...

    Text Solution

    |

  8. In a question a student was given to find the derivative of the prod...

    Text Solution

    |

  9. A nonzero polynomial with real coefficient has the property that f(x)=...

    Text Solution

    |

  10. If 'f' is an increasing function from RtoR such that f^(prime)prime(x)...

    Text Solution

    |

  11. If x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t) then x((dy)/(dx))^(3)-(dy)/(...

    Text Solution

    |

  12. Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly...

    Text Solution

    |

  13. If f(x)={sin((a-x)/2)t a n[(pix)/(2a)] for x > a and ([cos((pix)/(2a...

    Text Solution

    |

  14. Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):}. If f...

    Text Solution

    |

  15. Statement 1: Minimum number of points of discontinuity of the functi...

    Text Solution

    |

  16. Let f(x)=[tanx[cotx]], x in [(pi)/(12),(pi)/(2)), (where [.] denotes t...

    Text Solution

    |

  17. Let f[-2,2]rarrR be a continuous function such that f(x)assumes only i...

    Text Solution

    |

  18. If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)); then (f(101))/(f'(101))=

    Text Solution

    |

  19. A curve in the xy-plane is parametrically given by x=t+t^3a n dy=t^2,w...

    Text Solution

    |

  20. Number of points of discontinuity of f(x)=[sin^(-1)x]-[x] in its domai...

    Text Solution

    |