Home
Class 12
MATHS
underset(xto0)lim[(sin(sgn(x)))/((sgn(x)...

`underset(xto0)lim[(sin(sgn(x)))/((sgn(x)))],` where `[.]` denotes the greatest integer function, is equal to

A

0

B

1

C

`-1`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    DISHA PUBLICATION|Exercise Exercise- 1 : Concept Builder (Topic 4)|15 Videos

  • JEE MAIN - 2019 (HELD ON: 9TH APRIL 2019(MORNING SHIFT))

    DISHA PUBLICATION|Exercise MCQs|30 Videos

  • LINEAR INEQUALITIES

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

lim_(xto0) [(sin(sgn(x)))/((sgn(x)))], where [.] denotes the greatest integer function, is equal to

("lim")_(xvec0)[(sin(sgn(x)))/((sgn(x)))], where[dot] denotes the greatest integer function, is equal to 0 (b) 1 (c) -1 (d) does not exist

lim_(xto0)[(-2x)/(tanx)] , where [.] denotes greatest integer function is

lim_(x rarr1)(x sin(x-[x]))/(x-1) ,where [.]denotes the greatest integer function, is

lim_(xrarr oo) (logx)/([x]) , where [.] denotes the greatest integer function, is

lim_(x->0) ([(-5sinx)/x]+[(6sinx)/x] .(where [-] denotes greatest integer function) is equal to

int_(0)^(2pi)[|sin x|+|cos x|]dx , where [.] denotes the greatest integer function, is equal to :

lim_(x rarr0^(-))([x])/(x) (where [.] denotes greatest integer function) is

lim_(x rarr(5 pi)/(4))[sin x+cos x], where I] denotes the greatest integer function is equal to

DISHA PUBLICATION-LIMITS AND DERIVATIVES-Exercise -2 : Concept Applicator
  1. Evaluate underset(x to pi/4)lim (1-sin 2x)/(1+cos 4x)

    Text Solution

    |

  2. For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+....x^(2)/2+x+1, f...

    Text Solution

    |

  3. The value of lim(xto0)((4^x-1)^3)/(sin.(x^2)/(4)log(1+3x)),is

    Text Solution

    |

  4. If f(x) + f(y) = f((x+y)/(1-xy)) for all x, y in R (xy ne 1) and under...

    Text Solution

    |

  5. Evaluate underset(xto2)lim(x^(2)-x-2)/(x^(2)-2x-sin(x-2)).

    Text Solution

    |

  6. underset(n to oo)lim {1/(1-n^(2))+(2)/(1-n^(2))+....+(n)/(1-n^(2))} is...

    Text Solution

    |

  7. If zr=cos(pialpha)/(n^2)+isin(ralpha)/(n^2), where r=1,2,3....,n, then...

    Text Solution

    |

  8. If f(x)={{:(,|x|+1, x lt 0),(, 0,x=0),(,|x|-1, x gt 0):}" then "unders...

    Text Solution

    |

  9. The value of underset(theta to -pi/4)lim (cos theta +sin theta)/(theta...

    Text Solution

    |

  10. Let f(2)=4 and f'(2)=4. Then lim(x->2)(xf(2)-2f(x))/(x-2) is equal to

    Text Solution

    |

  11. The integer n for which lim(x rarr 0) ((cos x-1) ( cos x - e^x))/x^n i...

    Text Solution

    |

  12. The value f underset(x to pi/2)lim [1^(1//cos^(2)x)+2^(1//cos^(2) x)+....

    Text Solution

    |

  13. The value of underset(x to 2)lim (sqrt(1+sqrt(2+x))-sqrt3)/(x-2) is

    Text Solution

    |

  14. (lim)(xvec0)(sin(picos^2x))/(x^2) is equal to (1) pi/2 (2) 1 (3) ...

    Text Solution

    |

  15. If underset(x to 0)lim (x^(-3) sin 3x+ax^(-2) +b) exists and is equal ...

    Text Solution

    |

  16. If d/(dx)((1+x^4+x^8)/(1+x^2+x^4))=ax^3+bx,then

    Text Solution

    |

  17. For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+....x^(2)/2+x+1, f...

    Text Solution

    |

  18. lim ( x to pi//2 ) ( sec x - tan x ) is equal to

    Text Solution

    |

  19. underset(xto0)lim[(sin(sgn(x)))/((sgn(x)))], where [.] denotes the gre...

    Text Solution

    |

  20. If f(x)=|cos x|, then f' ((3pi)/(4)) is equal to

    Text Solution

    |