Home
Class 11
MATHS
If [x] denotes the greatest integer less...

If [x] denotes the greatest integer less than or equal to x, then evaluate `lim_(ntooo) (1)/(n^(3))([1^(2)x]+[2^(2)x]+[3^(2)x]+...+[n^(2)x]).`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If [x] denotes the greatest integer less than or equal to x, then evaluate lim_(ntooo) (1)/(n^(2))([1.x]+[2.x]+[3.x]+...+[n.x]).

[x] denotes the greatest integer, less than or equal to x, then the value of the integral int_(0)^(2)x^(2)[x]dx equals

if [x] denotes the greatest integer less than or equal to x then integral int_0^2x^2[x] dx equals

let [x] denote the greatest integer less than or equal to x. Then lim_(xto0) (tan(pisin^2x)+(abs(x)-sin(x[x]))^2)/x^2

Let [x] denote the greatest integer less than or equal to x, then the value of the integral int_(-1)^(1)(|x|-2[x])dx is equal to-

Let [x] denotes the greatest integer less then or equal to x. If x=(sqrt3+1)^5 , then [x] is equal to

Let [x] denote the greatest integer less than or equal to x for any real number x. Then lim_(n to oo) ([n sqrt(2)])/(n) is equal to

Let [ x ] denote the greatest integer less than or equal to x, then the value of the integral int_-1^1 (absx - 2[x]) dx is equal to

If a and b are positive and [x] denotes greatest integer less than or equal to x, then find lim_(xto0^(+)) x/a[(b)/(x)].

If [x] denotes the greatest integer less than or equal to x, the extreme values of the function f(x)=[1+sinx]+[1+sin2x]+[1+sin3x]+…+[1+sin nx], n in 1^+, x in(0,pi) are

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate underset(xtooo)lim((x^(2)+x-1)/(3x^(2)+2x+4))^((3x^(2)+x)/(x-...

    Text Solution

    |

  2. L=lim(x to a)(|2sinx-1|)/(2sinx-1)dotT h e n (a) limit does not exis...

    Text Solution

    |

  3. If [x] denotes the greatest integer less than or equal to x, then eval...

    Text Solution

    |

  4. f(x)=("lim")(n->oo)x/(x^(2n)+1)dotT h e n , A. f(1^+)+f(1^(-1))...

    Text Solution

    |

  5. Evaluate the limit: lim(x->1)((2x-3)(sqrt(x)-1))/(2x^2)

    Text Solution

    |

  6. ("lim")(ntooo)sum(x=1)^(20)cos^(2n)(x-10) is equal to

    Text Solution

    |

  7. underset(xto1)lim(1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

    Text Solution

    |

  8. f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim(x->oo)f(x) is equal...

    Text Solution

    |

  9. lim(ntooo) {((n)/(n+1))^(alpha)+"sin"(1)/(n)}^(n) (where alphainQ) is ...

    Text Solution

    |

  10. The value of underset(xto2)lim(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))...

    Text Solution

    |

  11. If underset(ntooo)lim(n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then ...

    Text Solution

    |

  12. If ("lim")(xveca)[f(x)g(x)] exists, then both ("lim")(xveca)f(x)a n d(...

    Text Solution

    |

  13. If f(x)=underset(ntooo)limn(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) i...

    Text Solution

    |

  14. lim(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

    Text Solution

    |

  15. underset(xto1)lim[cosec(pix)/(2)]^(1//(1-x)) (where [.] represents the...

    Text Solution

    |

  16. Given lim(x to 0)(f(x))/(x^(2))=2, where [.] denotes the greatest inte...

    Text Solution

    |

  17. Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not gr...

    Text Solution

    |

  18. Use formula lim(x->0)(a^x-1)/x=log(a) to find lim(x->0)(2^x-1)/((1+x)^...

    Text Solution

    |

  19. Evaluate : lim(x to 0) {tan(pi/4+x)}^(1/x)

    Text Solution

    |

  20. f(x) is the integral of (2sinx-sin2x)/(x^3),x!=0. Find lim(x->0)f^...

    Text Solution

    |