Home
Class 12
MATHS
If f(x)=((a+x)/(b+x))^(a+b+2x), then pro...

If `f(x)=((a+x)/(b+x))^(a+b+2x)`, then prove that `f'(0)=[2log""(a)/(b)+(b^2-a^2)/(ab)]((a)/(b))^(a+b)`.

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2017

    CHHAYA PUBLICATION|Exercise UNIT -4|8 Videos

  • QUESTION PAPER 2017

    CHHAYA PUBLICATION|Exercise UNIT -5|2 Videos

  • QUESTION PAPER 2017

    CHHAYA PUBLICATION|Exercise UNIT -2|7 Videos

  • QUESTION PAPER -2018

    CHHAYA PUBLICATION|Exercise WBJEE|45 Videos

  • QUESTIONS PAPER -2019

    CHHAYA PUBLICATION|Exercise WBJEE 2019|45 Videos

Similar Questions

Explore conceptually related problems

If f(x)=((a+x)/(b+x))^(a+b+2x) , prove that, f'(0) =[2"log"(a)/(b) +(b^(2)-a^(2))/(ab)]((a)/(b))^(a+b) .

If f(x)=(a(x-b))/(a-b)+(b(x-a))/(b-a) , then prove that f(a) + f(b) = a + b.

If f(x)=a(x-b)/(a-b)+b.(x-a)/(b-a) then show that f(a)+f(b)=f(a+b).

If g(x)=(x-a)/(x)+(x)/(x-b) , prove that, g((a+b)/(2))=(4ab)/(a^2-b^2)

If f(a+b-x)=f(x), then prove that int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot

If f(a+b-x)=f(x), then prove that int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot

If y^2=x z and a^x=b^y=c^z , then prove that (log)_ab=(log)_bc

If f(x)=e^(x+a) , g(x)=x^(b^2) and h(x)=e^(b^2x) ,show that (g[f(x)])/(h(x))=e^(ab^2)

If a^2+b^2 =7ab, then prove that "log"((a+b)/3)=1/2("log"a+"log"b)

CHHAYA PUBLICATION-QUESTION PAPER 2017-UNIT -3
  1. The value of int(-a)^(a)(xe^(x^4))/(1+x^2)dx is

    Text Solution

    |

  2. The degree of the differential equation (d^3y)/(dx^3)+y=root3(1+(dy)/(...

    Text Solution

    |

  3. If x=sqrt(a^(sin^(-1)t)" and "y=sqrt(a^(cos^(-1)t) show that (dy)/(dx)...

    Text Solution

    |

  4. Varify Rolle's theorem for the function f(x)=x^2-4x+3 in 1lexle3.

    Text Solution

    |

  5. Evalute: int (cosx-cos2x)/(1-cosx)dx.

    Text Solution

    |

  6. A particle starts with the velocity u and moves in a straight line, it...

    Text Solution

    |

  7. Find the interval where f(x)=(1)/(1+x^2) decreases.

    Text Solution

    |

  8. If f(x)=f(a+x), then prove that the value of int(a)^(a+t) f(x)dx is i...

    Text Solution

    |

  9. If f(x)=((a+x)/(b+x))^(a+b+2x), then prove that f'(0)=[2log""(a)/(b)+(...

    Text Solution

    |

  10. [(3,-2),(6,-k)] =A,also detA=0 then find k.

    Text Solution

    |

  11. intcos^(- 1)sqrt(x/(a+x))dx

    Text Solution

    |

  12. Evalute int (xdx)/(x^4-x^2+1)

    Text Solution

    |

  13. Solve: ydx-(x+2y^2)dy=0.

    Text Solution

    |

  14. In a certain culture the rate of increment of bactreria at any instant...

    Text Solution

    |

  15. Evalute: int(0)^((pi)/(4)) log(1+tantheta)d theta.

    Text Solution

    |

  16. From the definition of the definite integral, find the value of int(1...

    Text Solution

    |

  17. Using calculus, find the maximum value of the function ((x)/(a))^x .

    Text Solution

    |

  18. Using integration, prove that the area of the closed region bounded by...

    Text Solution

    |

  19. If the staight line (x)/(h)+(y)/(k)=1touches the curve ((x)/(a))^n+((y...

    Text Solution

    |

  20. Solve: xdy-ydx=sqrt(x^2+y^2)dx.

    Text Solution

    |