Home
Class 12
MATHS
Let A(n) between area bounded by the cur...

Let `A_(n)` between area bounded by the curve `y=(tan x)^(n),n in N` and the lines y = 0 and `x=(pi)/(4)`. For `n gt 2`, prove that `A_(n)+A_(n-2)=(1)/(n-1)` and decuce that `(1)/(2n+2)lt A_(n)lt (1)/(2n-2)`

Promotional Banner

Topper's Solved these Questions

  • AREAS

    AAKASH SERIES|Exercise Exercise-3.1|53 Videos

  • APPENDICES (REVISION EXERCISE)

    AAKASH SERIES|Exercise Sequence and series|12 Videos

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 1.4 (Level-2) |36 Videos

Similar Questions

Explore conceptually related problems

a_(n) = (n-1) (n-2) then a_(2) = ……….

Let A_(n) be the area enclosed by n^(th) orbit in the H-atoms. The graph ln ((A_(n))/(A_(l))) against ln(n)

If a_(n) = (n(n+3))/(n+2) , then find a_(17) .

Let P(n) : 1+ (1)/(4) + (1)/(9) + …. + (1)/(n^2) lt 2 - (1)/( n) is true for

If the general solution of sin 5x = cos 2x is of the form a_(n),(pi)/(2)" or "n=0, pm 1, pm2,....," then "a_(n)=

Lt_(ntooo){(1)/(2n+1)+(1)/(2n+2)+(1)/(2n+3)+..........+(1)/(2n+n)}=

If 0 lt y lt 1 , then sum_(n=1)^(oo)(1)/(2n-1)*y^(n+1)=……

If a_(K)=(1)/(K(K+1)) for K=1, 2, 3....n , then (sum_(K=1)^(n)a_(K))^(2)=

Lt_(ntooo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

Using mathematical induction, the numbers a_(n)'s are defined by, a_(0) =1, a_(n+1) = 3n^(2) + n+a_(n) ( n ge 0) . Then a_(n) =

AAKASH SERIES-AREAS-Exercise-3.2
  1. Find the area of the region bounded by the curves y= e^(x),y= e^(-x) a...

    Text Solution

    |

  2. Find the area of the region bounded by y=3^(x) and the lines y = 3 and...

    Text Solution

    |

  3. Find the area of the region enclosed by the parabola y=x^(2) + 2, the ...

    Text Solution

    |

  4. Find the area enclosed by the curves y= l nx, y= 2^(x) and the lines x...

    Text Solution

    |

  5. Find area enclosed by |y|=1-x^(2).

    Text Solution

    |

  6. Find the area enclosed between y= sqrt(5-x^(2)) and the lines y= |x-1|

    Text Solution

    |

  7. Find the ratio in which the area bounded by the curves y^(2)=12x and x...

    Text Solution

    |

  8. Find the ratio of the curves into which the circle x^(2) + y^(2)= 64 i...

    Text Solution

    |

  9. The area of the region bounded by the curves y=2^(x),y=2x-x^(2) and th...

    Text Solution

    |

  10. Find the area of the region bounded by the curves y= x^(2) and y= (2)/...

    Text Solution

    |

  11. The area bounded by the curves y=xe^(x),y=xe^(-x) and line x=1, is

    Text Solution

    |

  12. Find the area of the region bounded by the lines y=|x-1| and y=3-|x|

    Text Solution

    |

  13. Find the area of the region bounded by the curves x=|y^(2)-1| and y=x-...

    Text Solution

    |

  14. Find the are of the region bounded by y= log(e )x and y= sin^(4) (pi x...

    Text Solution

    |

  15. Find the area of the region bounded by 4y=|4-x^(2)| and y=7-|x|

    Text Solution

    |

  16. Find the area enclosed by y=log(e)(x+e) and x=log(e)((1)/(y)) and the ...

    Text Solution

    |

  17. Let f(x)= "max" {sin x, cos x, (1)/(2)}. Determine the area of the reg...

    Text Solution

    |

  18. Let f(x)=" max "{x^(2),(1-x)^(2),2x(1-x)} where 0le x le 1. Determine ...

    Text Solution

    |

  19. Let A(n) between area bounded by the curve y=(tan x)^(n),n in N and th...

    Text Solution

    |

  20. Find the area bounded by the curves y= cos x and y= sin x between the ...

    Text Solution

    |