Home
Class 12
MATHS
Evaluate lim(n->oo) [1^2/(n^3+1^3) + 2^2...

Evaluate` lim_(n->oo) [1^2/(n^3+1^3) + 2^2/(n^3+2^3) +3^2/(n^3+3^3) +..... 1/(2n) ]`

A

`(1)/(3).log 3`

B

`(1)/(3).log 2`

C

`(1)/(3).log.(1)/(3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION - DEFINITE INTEGRALS

    MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS (PREVIOUS YEARS (MHT-CET EXAM QUESTIONS))|12 Videos

  • INTEGRATION - DEFINITE INTEGRALS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|20 Videos

  • INTEGRATION - DEFINITE INTEGRALS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|20 Videos

  • DIFFERENTIATION

    MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS (TEST YOUR GRASP - II : CHAPTER 11)|24 Videos

  • INTEGRATION - INDEFINITE INTEGRALS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|45 Videos

Similar Questions

Explore conceptually related problems

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

lim_(n rarr oo) (1^2/(1-n^3)+2^2/(1-n^3)+...+n^2/(1-n^3))=

Evaluate: lim_(n rarr oo)((1^(2))/(n^(3))+(2^(2))/(n^(3))+(3^(2))/(n^(4))+...+(1)/(n))

Evaluate lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).

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

evaluate lim_ (n rarr oo) [(1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (2)) + ......... + (1) / (3 ^ (n))]

lim_ (n rarr oo) [(1 ^ (2)) / (n ^ (3) + 1 ^ (3)) + (2 ^ (2)) / (n ^ (3) + 2 ^ (3)) + (3 ^ (2)) / (n ^ (3) + 3 ^ (3)) + ... * (1) / (2n)]

Prove that lim_ (n rarr oo) ((1 ^ (2)) / (n ^ (3)) + (2 ^ (2)) / (n ^ (3)) + (3 ^ (2)) / ( n ^ (3)) + .... + (n ^ (2)) / (n ^ (3))) = (1) / (3)

MARVEL PUBLICATION-INTEGRATION - DEFINITE INTEGRALS -MULTIPLE CHOICE QUESTIONS (PART - B : Mastering The BEST)
  1. Let a, b and c be non - zero real numbers such that int (0)^(3) (3ax...

    Text Solution

    |

  2. lim(n to oo)[(n)/(1+n^(2))+(n)/(4+n^(2))+(n)/(9+n^(2))+…+(1)/(2n^2)]=

    Text Solution

    |

  3. Evaluate lim(n->oo) [1^2/(n^3+1^3) + 2^2/(n^3+2^3) +3^2/(n^3+3^3) +......

    Text Solution

    |

  4. lim(n->oo)1/nsum(r=1)^(2n)r/(sqrt(n^2+r^2)) equals

    Text Solution

    |

  5. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

    Text Solution

    |

  6. The solution for x of the equation int(sqrt(2))^x(dt)/(tsqrt(t^2-1))=p...

    Text Solution

    |

  7. integrate int0^(2pi) e^x . sin (pi/4 + x/2) dx

    Text Solution

    |

  8. Evaluate : int0^(pi/2)(2logsinx-logsin2x)\ dx

    Text Solution

    |

  9. If int0^(pi)xf(sinx)dx=Aint0^(pi/2)f(sinx)dx, then A is

    Text Solution

    |

  10. The integral underset(0)overset(a)int (g(x))/(f(x)+f(a-x))dx vanishes...

    Text Solution

    |

  11. If I(n)=underset(0)overset(pi//4)inttan^(n)x dx, then (1)/(I(2)+I(4)...

    Text Solution

    |

  12. The value int(-2)^(2) (plog ((1+x)/(1-x)) + q log ((1-x)/(1+x))^(-2) +...

    Text Solution

    |

  13. lim(n to oo)((sum(r=1)^(n)r^(2))(sum(r=1)^(n)r^(3)))/((sum(r=1)^(n)r^(...

    Text Solution

    |

  14. If : int(0)^(pi)ln(sin x) dx = k, then : int(0)^(pi//4)ln (1+tan x)=

    Text Solution

    |

  15. int(pi/3)^(pi/2) sqrt(1+cosx)/(1-cosx)^(5/2) dx

    Text Solution

    |

  16. int(-pi//2)^(pi//2)(sin^(2)x.cos^(2)x(sin x+cos x))dx=

    Text Solution

    |

  17. If : int(ln 2)^(x)(1)/(sqrt(e^(t)-1))dt=(pi)/(6), then : x =

    Text Solution

    |

  18. int(0)^(pi//2)sin x.cos x. sqrt(a^(2).sin^(2)x+b^(2).cos^(2)x)dx=

    Text Solution

    |

  19. If int0^oo (x^2 \ dx)/((x^2+a^2)(x^2+b^2)(x^2+c^2)) = pi/(2(a+b)(b+c)(...

    Text Solution

    |

  20. int(0)^(2) (2x-2)/(2x-x^(2)) dx is equal to

    Text Solution

    |