Home
Class 12
MATHS
Evaluate: ("lim")(n rarr oo)(1/(sqrt(4n^...

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

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

lim_(n rarr oo)2^(1/n)

lim_(n rarr oo)(3+sqrt(n))/(sqrt(n))

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

lim_(n rarr oo)n[sqrt(n+1)-sqrt(n))]

lim_(n->oo)[1/sqrt(2n-1^2) +1/sqrt(4n-2^2)+1/sqrt(6n-3^2)+...+1/n]

underset(nrarroo)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)))]

The value of ("lim")_(n rarr oo)sum_(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+sqrt(n))^2) is equal to

Evaluate : lim_(n to oo)[(sqrt(n))/((3+4sqrt(n))^(2))+(sqrt(n))/(sqrt(2)(3sqrt(2)+4sqrt(n))^(2))+(sqrt(n))/(sqrt(3)(3sqrt(3)+4sqrt(n))^(2))+.......+(1)/(49n)]

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

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

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Evaluate: inta^b x^3dx

    Text Solution

    |

  2. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|+pi/3))dx

    Text Solution

    |

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

    Text Solution

    |

  4. If y(x)=int(pi^2/16)^(x^2)(cosxcossqrt(theta))/(1+sin^2sqrt(theta))d t...

    Text Solution

    |

  5. Evaluate: ("lim")(nvecoo)[1/(n^2)sec^2 1/(n^2)+2//n^2sec^2 4/(n^2)++1/...

    Text Solution

    |

  6. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

    Text Solution

    |

  7. Evaluate ("lim")(n rarr oo)sum(k=1)^nk/(n^2+k^2)

    Text Solution

    |

  8. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

    Text Solution

    |

  9. Prove that pi/6 lt int0^1(dx) (sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

    Text Solution

    |

  10. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  11. Prove that int0^x e^(x t-t^2) dt=e^(x^(2)/4)int0^x e^-(t^(2)/4)dt

    Text Solution

    |

  12. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

  13. Evaluate int(-4)^(-5)e^((x+5)^(2))dx+3int(1//3)^(2//3)e^(9(x-2/3)^(2))...

    Text Solution

    |

  14. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

    Text Solution

    |

  15. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/x

    Text Solution

    |

  16. If for a real number y ,[y] is the greatest integral function less, th...

    Text Solution

    |

  17. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/(1+x^2)

    Text Solution

    |

  18. int0^x{int0^uf(t)dx}\ du is equal to (a) int0^x(x-u)f(u)du (b) int0...

    Text Solution

    |

  19. Compute the integrals: int(1/e)^e1/xsin(x-1/x)dx

    Text Solution

    |

  20. STATEMENT 1: int0^pixsinxcos^2xdx=pi/2int0^pisinxcos^2x dx. STATEMEN...

    Text Solution

    |