Home
Class 12
MATHS
Given a real valued function f such that...

Given a real valued function f such that `f(x)={tan^2[x]/(x^2-[x]^2) , x lt 0 and 1 , x=0 and sqrt({x}cot{x}) , x lt 0` where [.] represents greatest integer function then

A

`underset( x rarr0 ) ( "lim") f(x) = 1`

B

`underset( x rarr 0^(-1)) ( "lim") f(x) = cot 1 `

C

`cot^(-1)( underset( x rarr 0^(-))("lim")f(x))^(2) = 1 `

D

f is continuous at x =0

Text Solution

Verified by Experts

The correct Answer is:
C
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

Given a real valued function f such that f(x)={(tan^(2)[x])/(x^(2)-[x]^(2)),x<0 and 1,x=0 and sqrt({x}cot{x}),x<0 where [.] represents greatest integer function then

If f(x)=([x])/(|x|), x ne 0 , where [.] denotes the greatest integer function, then f'(1) is

If f(x)=([x])/(|x|),x ne 0 where [.] denotes the greatest integer function, then f'(1) is

lim_(x rarr0)(tan^(2)[x])/([x]^(2)), where [] represents greatest integer function,is

Find x satisfying [tan^(-1)x]+[cot^(-1)x]=2 where [| represents the greatest integer function.

lim_(xrarr0) [(100 tan x sin x)/(x^2)] is (where [.] represents greatest integer function).

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

If x^(2)+x+1-|[x]|=0, then (where [.] is greatest integer function) -

f:(2,3)rarr(0,1) defined by f(x)=x-[x], where [.] represents the greatest integer function.

f(x)=1+[cos x]x, in 0<=x<=(x)/(2) (where [.] denotes greatest integer function)

MOTION-LIMIT-EXERCISE -1
  1. lim(x -> 1) (1- x + [x-1] + [1-x]) = where [.] denotes the greatest in...

    Text Solution

    |

  2. lim(x -> 0)[sin[x-3]/([x-3])] where [.] denotes greatest integer funct...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |