Home
Class 12
MATHS
If [x] is the greatest integer function,...

If [x] is the greatest integer function, then
`underset (x to 2^+)lim ([x]^3/3-[x/3]^3)=`

A

0

B

`(64)/(27)`

C

`8/3`

D

`7/3`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TS EAMCET 2019 (3 MAY SHIFT 1)

    TS EAMCET PREVIOUS YEAR PAPERS|Exercise Mathematics|79 Videos
  • TS EAMCET 2019 (4 MAY SHIFT 2)

    TS EAMCET PREVIOUS YEAR PAPERS|Exercise MATHEMATICS|80 Videos

Similar Questions

Explore conceptually related problems

underset(x to 3)"Lt" [x]=

If [.] denotes the greatest integer functon, then Lt_(n to oo)([1^(3)x]+[2^(3)x]+....+..[n^(3)x])/(n^(4))

underset(x to 3)"Lt"|x|

If [x] denotes the greatest integer le x , then underset(n rarr oo)lim(1)/(n^(3)){[1^(2)x]+[2^(2)x]+[3^(2)x]+...+[n^(2)x]}=

underset(x to oo)lim (-x^(3)+8)/(2x^(2)+5x+7)=

underset(x to 2)"Lt" (x^(5)-32)/(x^(3)-8)=

If [x] denotes the greatest integer function, then the domain of the function f(x)=sqrt((x-[x])/(log (x^(2)-x))) is

underset(x to oo)lim (sqrt(3x^(2)+5))/(5x+3)=

TS EAMCET PREVIOUS YEAR PAPERS-TS EAMCET 2019 (3 MAY SHIFT 2)-MATHEMATICS
  1. If A(3,2,3), B (1,4,6) and C (7,4,5) are the three vertices of a paral...

    Text Solution

    |

  2. pi1 is a plane passing through the point (1,2,3) and perpendicular to ...

    Text Solution

    |

  3. If [x] is the greatest integer function, then underset (x to 2^+)lim...

    Text Solution

    |

  4. If the function defined by f(x) ={{:((x^2+e^(1/(2-x)))^(-1)),(" ...

    Text Solution

    |

  5. If {{:(ax+b , if x le1),(ax^2+c, if 1 lt x le 2),((dx^2+1)/x,if x ge 2...

    Text Solution

    |

  6. Suppose f(x) = e^(-sqrtx) +e^(-1/(x^2)). If f^('') = alpha e^(-sqrtx...

    Text Solution

    |

  7. The derivative of cos h ^(-1) x with respect to log x at x=5 is

    Text Solution

    |

  8. A right solid circular cylinder of given volume will have the least to...

    Text Solution

    |

  9. The smaller side of the rectangle with the largest area, that can be i...

    Text Solution

    |

  10. Let a,b,c in R be such that 2a +3b +6c =0 and g(x) be the anti deriv...

    Text Solution

    |

  11. Let f(x) = (x-3) ^(2018) (2-x)^(2019) , x in R . If (alpha) is a relat...

    Text Solution

    |

  12. int sin ^(-1) sqrt(-x/(a+x))dx=

    Text Solution

    |

  13. int (x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx=

    Text Solution

    |

  14. int (log (sin x) +x cot x)dx =

    Text Solution

    |

  15. If int(2x^2)/((2x^2+alpha)(x^2+5))dx =sqrt(5)/3 tan^(-1)"" x/sqrt2 +...

    Text Solution

    |

  16. If int0^3 (3x^2-4x+2)dx =k then a root of 3x^2-4x+2 = (3k)/5 that lies...

    Text Solution

    |

  17. If int 0 ^(2a) x^2 sqrt(2ax-x^2)dx = ka ^4 then k : pi=

    Text Solution

    |

  18. The area of the region (in square units ) bounded by the curves y= x^3...

    Text Solution

    |

  19. If the order of a differential equation (d^2y)/(dx^2)-2 ((dy)/(dx))^...

    Text Solution

    |

  20. The solution of the differential equation ydx -xdy +3 x^2y^2e^x""^3 dx...

    Text Solution

    |