Home
Class 12
MATHS
f'(0) = lim(n->oo) nf(1/n) and f(0)=0 U...

`f'(0) = lim_(n->oo) nf(1/n) and f(0)=0` Using this, find `lim_(n->oo)((n+1)(2/pi)cos^(- 1)(1/n)-n)),|cos^(-1)1/n|

Promotional Banner

Topper's Solved these Questions

  • Maxima and Minima

    A DAS GUPTA|Exercise EXERCISE|59 Videos
  • Objective Tests

    A DAS GUPTA|Exercise Exercise|36 Videos

Similar Questions

Explore conceptually related problems

FInd lim_(n rarr oo)(2n-1)2^(n)(2n+1)^(-1)2^(1-n)

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

If |cos^-1(1)/(n)|lt (pi)/(2) , then lim_(n to oo) {(n+1)(2)/(pi)cos^-1.(1)/(n)-n}

If A=[{:(,1,a),(,0,1):}] then find lim_(n-oo) (1)/(n)A^(n)

Find lim_ (n rarr oo) n ^ (n) (1 + n) ^ (- n)

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

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

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

" (e) "lim_(n rarr oo)[(n!)/(n^(n))]^(1/n)

A DAS GUPTA-Miscellaneous Exercises-Exercise
  1. f: [0.4]-> R is a differentiable function. Then prove that for some a,...

    Text Solution

    |

  2. Given a function f:[0,4]toR is differentiable ,then prove that for som...

    Text Solution

    |

  3. If f: R to [0,∞) be a function such that f(x -1) + f(x + 1) = sqrt3(f...

    Text Solution

    |

  4. Using Rolles theorem, prove that there is at least one root in (45^(1/...

    Text Solution

    |

  5. A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)...

    Text Solution

    |

  6. Find the equation of circle touching the line 2x + 3y + 1=0 at the poi...

    Text Solution

    |

  7. (int(sin^(3/2)x+cos^(3/2)x)dx)/(sqrt(sin^(3)x cos^(3)x sin(x-alpha)))

    Text Solution

    |

  8. T is a parallelepiped in which A,B,C and D are vertices of one face an...

    Text Solution

    |

  9. f'(0) = lim(n->oo) nf(1/n) and f(0)=0 Using this, find lim(n->oo)((...

    Text Solution

    |

  10. If y(x)=int(pi^2/16)^(x^2) (cosx cos sqrt(theta))/(1+sin^2 sqrt(theta)...

    Text Solution

    |

  11. At any point P on the parabola y^2 -2y-4x+5=0 a tangent is drawn which...

    Text Solution

    |

  12. If a DeltaABC remains always similar to a given triangle and the point...

    Text Solution

    |

  13. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

    Text Solution

    |

  14. if |f(x1)-f(x2)|<=(x1-x2)^2Find the equation of gent to the curve y= f...

    Text Solution

    |

  15. Find the equation of the common tangent to the circle x^2 + y^2 = 16 a...

    Text Solution

    |

  16. If [(4a^2,4a,1),(4b^2,4b,1),(4c^2,4c,1)][(f(-1)),(f(1)),(f(2))][(3a^2...

    Text Solution

    |

  17. The total number of runs scored If n matches is (n+1)/4(2^(n+1)-n-2),w...

    Text Solution

    |

  18. A square circumscribes the circle |z -1| = sqrt2. If one of the vertic...

    Text Solution

    |

  19. Evaluate int(0)^(pi)e^(|cosx|)(2"sin"(1/2cosx)+3"cos"(1/2cosx))sinx dx...

    Text Solution

    |

  20. If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x...

    Text Solution

    |