Home
Class 12
MATHS
Lim(x rarr 0^+) ((pi/2-cot^(-1){x})x)/("...

`Lim_(x rarr 0^+) ((pi/2-cot^(-1){x})x)/("sgn"x-cosx)` (where {.} and sgn(.) denotes fractional part function and signum function respectively) is equal to

A

2

B

1

C

0

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    MOTION|Exercise EXERCISE -2( LEVEL-I)|16 Videos
  • LIMIT

    MOTION|Exercise EXERCISE-2(LEVEL-2)|5 Videos
  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    MOTION|Exercise Exercise -4 Level -II|7 Videos
  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

Similar Questions

Explore conceptually related problems

lim_(x rarr0^(+))(((pi)/(2)-cot^(-1){x})x)/(sgn backslash x-cos x) (where {.} and sgn(.) denotes fractional part function and signum function respectively) is equal to

lim_(x rarr1)({x})^((1)/(n pi x)) ,where {.} denotes the fractional part function

If x in[2,3) ,then {x} equals, where {.} denotes fractional part function.

underset( x rarr0 ) ("lim") (sin [cos x ])/( 1+[cos x ] ) ( where {x} denotes fractional part function )

In which of the following function,range is not singleton set f(x)=[x]+[-x]( b) f(x)={x}+{-x}f(x)=|sgn(x)|(d)f(x)=[sqrt(x-[x]) where [x],{x}, and sgn(x) are greatest integer function,fractional part function and signum function respectively.

Let function f(x) is defined in [-2,2] as f(x)={{:({x}",",-2lexle-1),(|sgnx|",",-1lexle1),({-x}",",1ltxle2):} where {x} and sgn x denotes fractional part and signum functions, respectively. Then the area bounded by the graph of f(x) and x-axis is

Evaluate int _(-1) ^(15) Sgn ({x})dx, (where {**} denotes the fractional part function)

The number of integral values of x satisfying the equation sgn([(19)/(2+x^(2))])=[1+{5x}] (where [x],{x} and sgn(x) denote the greatest integer,the fractional part and the signum functions respectively is

Let a function f(x) be defined in [-2, 2] as f(x) = {{:({x}",",, -2 le xlt -1), (|"sgn "x|",",,-1le x le 1),({-x}",",, 1 lt xle 2):} where {x} and sgn x denote fractional part and signum functions, respectively. Then find the area bounded by the graph of f(x) an the x-axis.

MOTION-LIMIT-EXERCISE -1
  1. Given a real valued function f such that f(x)={tan^2[x]/(x^2-[x]^2) ,...

    Text Solution

    |

  2. underset( x rarr0 ) ("lim") (sin [cos x ])/( 1+[cos x ] ) ( where ...

    Text Solution

    |

  3. Lim(x rarr 0^+) ((pi/2-cot^(-1){x})x)/("sgn"x-cosx) (where {.} and sgn...

    Text Solution

    |

  4. underset( x rarroo ) ("lim") sec^(-1) ((x)/( x+1)) =

    Text Solution

    |

  5. If f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", ...

    Text Solution

    |

  6. If f( 2010) = pi //2, f(2x) = f(x) AA x in R and f(x) is continuous f...

    Text Solution

    |

  7. underset( n rarr oo) ( "Lim") ( -3n + (-1)^(n))/(4n-(-1)^(n)) is

    Text Solution

    |

  8. lim(xto oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greate...

    Text Solution

    |

  9. Limit(n->oo) {(1+x) (1+x^2)(1+x^4).......(1+x^(2^n))}= if |x|<1 has th...

    Text Solution

    |

  10. The graph of the function f(x) = underset( t rarr 0 ) ("Lim") ((2x)/(p...

    Text Solution

    |

  11. Let f(x)=(loge(x^2+e^x))/(loge(x^4+e^2x)). If lim(xto oo) f(x)=l and l...

    Text Solution

    |

  12. If [x] denotes the greatest integer le x , then underset( n rarr oo ) ...

    Text Solution

    |

  13. lim(n->oo) 1/sqrt(n^2)+1/sqrt(n^2+1)+1/sqrt(n^2+2)+.....1/sqrt(n^2+2n)...

    Text Solution

    |

  14. The limit underset( theta rarr0 ) ("lim") ([ (nsin theta)/( theta) ]+ ...

    Text Solution

    |

  15. lim(x->-oo) {x^2*sin(1/x)}/sqrt(9x^2+x+1) is equal to

    Text Solution

    |

  16. lim(x->oo)(x^2sin(1/x)+x+1)/(x^2+x+1) is equal to

    Text Solution

    |

  17. Evaluate: ("lim")(nvecoo)ncos(pi/(4n))sin(pi/(4n)) where (x , y)vec(0...

    Text Solution

    |

  18. lim(x->pi/2) ((1-tan(x/2))(1-sinx))/((1+tan(x/2))((pi-2x)^3))

    Text Solution

    |

  19. The limit underset( x rarr0 ) ( "lim") ( 1- cos x sqrt( cos 2x))/( x^(...

    Text Solution

    |

  20. lim(x->0^+)cos^(- 1)(1-x)/(sqrt(x))

    Text Solution

    |