Home
Class 12
MATHS
Let f(x)=[x]+[-x], where [x] denotes the...

Let `f(x)=[x]+[-x]`, where `[x]` denotes the greastest integer less than or equal to x . Then, for any integer m

A

f is continuous at x=m

B

`lim_(x to m+)` f(x) exists and is equal to f(m)

C

`lim_(x tom)` f(x) exists but is not equal to f(m)

D

f is differentiable at x=m

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Solved Examples Level 2 (Single Correct Answer)|30 Videos

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Solved Examples (Numberical Answer)|16 Videos

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Solved Examples (Single Correct Answer)|10 Videos

  • JEE (MAIN) QUESTIONS WITH SOLUTIONS MATHEMATICS (7 TH JAN-MORNING )

    MCGROW HILL PUBLICATION|Exercise QUESTIONS|25 Videos

  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=[x^(2)]+[x+2]-8 , where [x] denotes the greater integer than or equal to x , then

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

If f(x)=|x-1|-[x] , where [x] is the greatest integer less than or equal to x, then

let f:R rarr R be given by f(x)=[x]^(2)+[x+1]-3, where [x] denotes the greatest integer less than or equal to x. Then,f(x) is

Let f(x)=(x-[x])/(1+x-[x]), where [x] denotes the greatest integer less than or equal to x,then the range of f is

Let f(x)=(x^(2)-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x), then

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

If the function f:R rarr R be such that f(x)=x-[x], where [x] denotes the greatest integer less than or equal to x, then f^(-1)(x) is

The function of f:R to R , defined by f(x)=[x] , where [x] denotes the greatest integer less than or equal to x, is

MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Solved Examples Level 1 (Single Correct Answer)
  1. underset(xtooo)lim[sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to

    Text Solution

    |

  2. If (lim)(x->-a)(x^9+a^9)/(x+a)9,\ find the real value of adot

    Text Solution

    |

  3. Let f(x)=[x]+[-x], where [x] denotes the greastest integer less than o...

    Text Solution

    |

  4. Let f(x) be a continuous function defined for 1 <= x <= 3. If f(x) tak...

    Text Solution

    |

  5. Let f(x)= {{:(|x| cos (1//x)+9x^2, xne 0),(k, x=0):} then f is cont...

    Text Solution

    |

  6. If f(x)=tan (pi//4 -x)//cot2x for x ne pi//4. The value of f(pi//4) so...

    Text Solution

    |

  7. Let a function f be defined by f(x)="x-|x|"/x for x ne 0 and f(0)=2. T...

    Text Solution

    |

  8. If f(x) is a continuous function satisfying f(x)f(1/x) =f(x)+f(1/x) an...

    Text Solution

    |

  9. The function f(x) = (x-1)^(1/((2-x)) is not defined at x = 2. The valu...

    Text Solution

    |

  10. Let f(x)=(x+x^2+.....+x^n-n)/(x-1), x!=1, then value of f(1) so that f...

    Text Solution

    |

  11. If f(u) = 1/(u^(2)+u-2) , where u = 1/(x-1) , then the points of dis...

    Text Solution

    |

  12. Let f(x) and phi(x) be defined by f(x)=[x] and phi(x)={0, x in I and...

    Text Solution

    |

  13. If a,b are chosen from {1,2,3,4,5,6,7} randomly with replacement. The ...

    Text Solution

    |

  14. The value of lim(xto pi//2)(cot x-cosx)/(pi-2x)^3 is

    Text Solution

    |

  15. If underset(x to 0)lim({(a-n)nx - tan x} sin nx)/x^(2) = 0, where n is...

    Text Solution

    |

  16. Find derivative of tan3x by first principle

    Text Solution

    |

  17. The value of lim(x to 0) (e^(nx)-(1+nx+n^2/2x^2))/x^3 (n gt 0) is

    Text Solution

    |

  18. Let f(x)=(e^(x)-1)^(2n)/(sin^n (x//a)(log (1+(x//a)))^n for x ne 0 . I...

    Text Solution

    |

  19. Let f(x)={{:(x+a,","x lt 0),(|x-1|,","x ge 0):} and g(x)={{:(x+1,", if...

    Text Solution

    |

  20. If f:RtoR is function defined by f(x) = [x]^3 cos ((2x-1)/2)pi , where...

    Text Solution

    |