Home
Class 12
MATHS
lim(xto oo) (logx^n-[x])/([x]) where n i...

`lim_(xto oo) (logx^n-[x])/([x])` where `n in N and [.]` denotes the greatest integer function, is

A

has value -1

B

has value 0

C

has value 1

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_(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greatest integer function, is

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

lim_(x->0) (lnx^n-[x])/[x], n in N where [x] denotes the greatest integer is

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

The value of lim_(xto0)(sin[x])/([x]) (where [.] denotes the greatest integer function) is

lim_(x -> 0)[sin[x-3]/([x-3])] where [.] denotes greatest integer function is

lim_(x rarr-1)([x]+|x|). (where [.] denotes the greatest integer function)

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

lim_(xto0)[m(sinx)/x] is equal to (where m epsilon I and [.] denotes greatest integer function)

MOTION-LIMIT-EXERCISE -1
  1. If f( 2010) = pi //2, f(2x) = f(x) AA x in R and f(x) is continuous f...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. underset( x rarr 0 ) ("lim") [ ( 1-e^(x)) ( sin x )/( |x|)] is equal ...

    Text Solution

    |

  17. Evaluate: underset(hrarr0)("lim")(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(...

    Text Solution

    |

  18. lim(x->0) sin(6x^2)/(lncos(2x^2-x)

    Text Solution

    |

  19. The value of underset( x rarr 0 ) ( "Lim") ( sin ( ln ( 1+ x)))/( ln (...

    Text Solution

    |

  20. underset( x rarr pi //2) ("Lim") ( 2 ^(cos x) - 1)/( x ( x-pi //2))= ...

    Text Solution

    |