Home
Class 11
MATHS
lim(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^...

`lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)`

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

lim_(nrarroo) {(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))} is equal to-

Evaluate: ("lim")_(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt(3n^2)))

lim_(n to oo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(nrarroo) [(1)/(n)+(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+...+(sqrt(n^(2)-(n-1)^(2)))/(n^(2))]

lim_(nrarroo) [(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]

Find the value of lim_(nrarroo)[(1)/(sqrt(2n-1)^(2))+(1)/(sqrt(4n-2^(2)))+...+(1)/(n)] .

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

Prove that underset( n rarr infty) lim[1/n+sqrt(n^2-1^2)/n^2+sqrt(n^2-2^2)/n^2+…..sqrt(n^2-(n-1)^2)/n^2] = pi/4

Find the value of underset(ntooo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

Evaluate: lim_(n->oo)n^2{sqrt((1-cos(1/n))sqrt((1-cos(1/n)) sqrt((1-cos(1/n)) ..oo)))}dot

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. lim(x->0)(e^(5x) - 1)/(3x)

    Text Solution

    |

  2. lim(x->(pi/2)) (1-sinx)tanx =

    Text Solution

    |

  3. The value of lim(x->3)((x^3+27)(log)e(x-2))/(x^2-9) is a. 9 b. 18 c....

    Text Solution

    |

  4. If (lim)(xvec0)(e^(a x)-e^x-x)/(x^2)=b (finite), then a=2,b=0 b. a=0,b...

    Text Solution

    |

  5. If underset(xrarr0)(lim)(x^3)/(sqrt(a+x)(bx-sinx))=1,agt0, then a+b is...

    Text Solution

    |

  6. underset(xrarr0)(lim)[(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the...

    Text Solution

    |

  7. The value of lim(x->pi/4) (sqrt(1-sqrt(sin2x)))/(pi-4x) is

    Text Solution

    |

  8. lim(x->0) (sin x /x)

    Text Solution

    |

  9. If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represents the gr...

    Text Solution

    |

  10. If A=underset(xrarr0)(lim)(sin^(-1)(sinx))/(cos^(-1)(cosx))and B=under...

    Text Solution

    |

  11. Let f(x)=lim(m->oo){lim(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then...

    Text Solution

    |

  12. lim(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional par...

    Text Solution

    |

  13. Let f(x)=(lim)(xvecoo)(tan^(-1)(tanx))/(1+((log)e x)^n),x!=(2n+1)pi/2 ...

    Text Solution

    |

  14. Assume that underset(thetararr-1)(lim)f(theta) exists and (theta^(2)+t...

    Text Solution

    |

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

    Text Solution

    |

  16. Let f: RvecR be such that f(a)=1,f^(prime)(a)=2. Then (lim)(xvec0)((...

    Text Solution

    |

  17. If f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"s...

    Text Solution

    |

  18. If a >0,b >0 then (lim)(n->oo)((a-1+b^(1/n))/a)^n= b^(1//a) b. a^...

    Text Solution

    |

  19. (lim)(xvec0)("log"(e^x^2+2sqrt(x)))/(t a nsqrt(x)) is equal to 0 b. 1 ...

    Text Solution

    |

  20. If f(x)=(lim)(nvecoo)(cos(x/(sqrt(n))))^n , then the value of (lim)(xv...

    Text Solution

    |