Home
Class 12
MATHS
Cauchys mean value theorem...

Cauchys mean value theorem

Text Solution

Verified by Experts

According to Cauchy's Mean Value Theorem , If there are two functions, `f(x)` and `g(x)` then these two functions shall be continuous on the interval, `[a,b]`, and these functions are differentiable on the range `(a,b)` , and `g′(x)≠0` for all `x∈(a,b)`.
Also Cauchy's Mean Value Theorem sums up the Lagrange's Mean Value Theorem.
Promotional Banner

Topper's Solved these Questions

  • MEAN AND VARIANCE OF A RANDOM VARIABLE

    RD SHARMA|Exercise Solved Examples And Exercises|113 Videos

  • PROBABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|422 Videos

Similar Questions

Explore conceptually related problems

Roots theory with illustration || Cauchy Mean Value Theorem || Equation based question

In [0,1] Largrange's mean value theorem is not application to

In [0, 1] Lagrange's mean value theorem is not applicable to

Using Lagranges mean value theorem,prove that |cos a-cos b|<=|a-b|

Using Lagranges mean value theorem,show that sin(:x for x:)0.

The value of C in Lagrange's mean value theorem for f(x)=lx^(2)+mx+n,(l!=0) on [a,b] is

Find the value of c in Lagrange's mean value theorem for the function f (x) = log _(e) x on [1,2].

The value of c in Largrange's mean value theorem for the function f(x)=x(x-2) when x in [1,2] is

RD SHARMA-MEAN VALUE THEOREMS-Solved Examples And Exercises
  1. Verify Lagranges mean value theorem for function f(x)=x^2+x-1 on [0...

    Text Solution

    |

  2. Discuss the applicability of Lagranges mean value theorem for the f...

    Text Solution

    |

  3. Show that the lagranges mean value theorem is not applicable to the...

    Text Solution

    |

  4. Find a point on the parabola y=(x-4)^2 , where the tangent is pa...

    Text Solution

    |

  5. Find a point on the curve y=x^2+x , where the tangent is paralle...

    Text Solution

    |

  6. Find a point on the parabola y=(x-3)^2 , where the tangent is pa...

    Text Solution

    |

  7. Find the points on the curve y=x^3-3x , where the tangent to the...

    Text Solution

    |

  8. Find a point on the curve y=x^3+1 where the tangent is parallel ...

    Text Solution

    |

  9. Let C be a curve defined parametrically as x=a\ cos^3theta , y=a\ si...

    Text Solution

    |

  10. If f(x)=A x^2+B x+C is such that f(a)=f(b) , then write the value o...

    Text Solution

    |

  11. State Rolle’s theorem.

    Text Solution

    |

  12. Cauchys mean value theorem

    Text Solution

    |

  13. Find the value of c prescribed by Lagranges mean value theorem for ...

    Text Solution

    |

  14. For the function f(x)=x+1/x ,\ \ x in [1,\ 3] , the value of c for the...

    Text Solution

    |

  15. The value of c in Rolles theorem when f(x)=2x^3-5x^2-4x+3 , is x in...

    Text Solution

    |

  16. When the tangent to the curve y=xlogx is parallel to the chord j...

    Text Solution

    |

  17. The value of c in Rolles theorem for the function f(x)=(x(x+1))/(e^...

    Text Solution

    |

  18. The value of c in Largrange's mean value theorem for the function f(...

    Text Solution

    |

  19. The value of c in Rolles theorem for the function f(x)=x^3-3x in th...

    Text Solution

    |

  20. If f(x)=e^xsinx in [0,\ pi] , then c in Rolles theorem is pi//6 (b) pi...

    Text Solution

    |