Home
Class 12
MATHS
The value of ("lim")(n rarr oo)sum(r=1)^...

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

A

`(1)/(35)`

B

`(1)/(14)`

C

`(1)/(10)`

D

`(1)/(5)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (More than one answer)|32 Videos

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Linked Comprehension Type Questions|11 Videos

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Competition level Questions|80 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

The value of ("lim")_(nvecoo)sum_(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+sqrt(n))^2) is equal to 1/(35) (b) 1/4 (c) 1/(10) (d) 1/5

The value of ("lim")_(nvecoo)sum_(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+sqrt(n))^2) is equal to 1/(35) (b) 1/4 (c) 1/(10) (d) 1/5

The value of lim_(n to oo) sum_(r=1)^(n)(r^(2))/(r^(3)+n^(3)) is -

The value of lim_(n to oo)sum_(r=1)^(n)(1)/(n) sqrt(((n+r)/(n-r))) is :

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

lim_(nrarroo) sum_(r=0)^(n-1) (1)/(sqrt(n^(2)-r^(2)))

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

The value of I=lim_(nrarroo)Sigma_(r=1)^(n)(r)/(n^(2)+n+r) is equal to

The value of lim_(n to oo)(1)/(n).sum_(r=1)^(2n)(r)/(sqrt(n^(2)+r^(2))) is equal to

l isum_(n-gtoo)sum_(r=1)^n1/(sqrt(4n^2-r^2))

AAKASH INSTITUTE ENGLISH-INTEGRALS-Objective Type Questions (Only one answer)
  1. The value of the definite integral int(19)^37((x)^2+3(sin2pix))dx wher...

    Text Solution

    |

  2. If l(n)=int(0)^((pi)/(4)) tan^(n) xdx show that (1)/(l(2)+l(4)),(1)/(l...

    Text Solution

    |

  3. The value of ("lim")(n rarr oo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r...

    Text Solution

    |

  4. underset(kto0) lim1/kint0^k(1+sin2x)^(1/x)dx

    Text Solution

    |

  5. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  6. Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex >...

    Text Solution

    |

  7. If f(x)=[{:(sqrt(1-x), , , 0 le x le 1),((7x-6)^(-1) , , ,1 le x le 2)...

    Text Solution

    |

  8. If f:RrarrR defined by f(x)=sinx+x, then find the value of int0^pi(f^-...

    Text Solution

    |

  9. The value of int0^100 [tan^-1 x]dx is, (where [*] denotes greatest in...

    Text Solution

    |

  10. Iff(x)={0,w h e r ex=n/(n+1),n=1,2,31,e l s e w h e r e t h e nt h ev...

    Text Solution

    |

  11. Let g(x) be a continous and differentiable function such that int(0...

    Text Solution

    |

  12. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

    Text Solution

    |

  13. f:(0,infty)rarrR and F(x)=int(0)^(x)t f(t)dt If F(x^(2))=x^(4)+x^(5)...

    Text Solution

    |

  14. int(-pi//4) ^(pi//4) x^(3) sin^(4) xdx=

    Text Solution

    |

  15. The value of int(-10)^(10)[{f(f(x)}+{f(f((1)/(x))}]dx, where f(x)=(1-x...

    Text Solution

    |

  16. The value of int(-2)^(2)(ax^(2011)+bx^(2001)+c)dx, where a, b, c are c...

    Text Solution

    |

  17. If for non zero x, 3f(x)+4f((1)/(x))=(1)/(x)-10, then the value of int...

    Text Solution

    |

  18. The value of int(2010pi+(pi)/(6))^(2010pi+(pi)/(3))(sinx+cosx)dx is

    Text Solution

    |

  19. Let int(a)^(b)f(x)dx=int(a+c)^(b+c)f(x-c)dx. Then the value of int(0)^...

    Text Solution

    |

  20. If x^(f(x))=e^(x-f(x)), then the value of integral int(1)^(2)f'(x){(1+...

    Text Solution

    |