Home
Class 12
MATHS
If a > b >0, with the aid of Lagr...

If `a > b >0,` with the aid of Lagranges mean value theorem, prove that `n b^(n-1)(a-b) < a^n -b^n < n a^(n-1)(a-b) , if n >1.` `n b^(n-1)(a-b) > a^n-b^n > n a^(n-1)(a-b) , if 0 < n < 1.`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

State Lagrange's mean value theorem.

Using Lagrange's mean value theorem prove that, e^(x) gt 1 +x

Using Lagranges mean value theorem, prove that |cosa-cosb|<=|a-b|dot

Using Lagranges mean value theorem, prove that |cosa-cosb|<=|a-b|dot

Using Largrange's mean value theorem, prove that, b^(n)-a^(n) gt n a^(n-1)(b-a)" when " b gt a .

Using Lagrange's mean value theorem prove that, log (1+x) lt x ("when " x gt 0)

Using Lagranges mean value theorem, prove that (b-a)/bltlog(b/a)lt(b-a)/a, where 0ltaltbdot

If from Lagrange's Mean Value theorem we have, f(4)-f(1)=(4-1)f'(c ) then -

Using lagrange's mean value theorem, show that (beta-alpha)/(1+beta^2) alpha > 0.

Let f(x)=e^(x), x in [0,1] , then the number c of Lagrange's mean value theorem is -

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Prove that |tan^(-1)x-tan^(-1)y|lt=|x-y|AAx , y in Rdot

    Text Solution

    |

  2. Using Lagranges mean value theorem, prove that (b-a)/bltlog(b/a)lt(b-a...

    Text Solution

    |

  3. If a &gt; b &gt;0, with the aid of Lagranges mean value theorem, prov...

    Text Solution

    |

  4. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

    Text Solution

    |

  5. If the tangent to the curve x y+a x+b y=0 at (1,1) is inclined at an a...

    Text Solution

    |

  6. Find the condition that the line A x+B y=1 may be normal to the curve ...

    Text Solution

    |

  7. Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y...

    Text Solution

    |

  8. If the equation of the tangent to the curve y^2=a x^3+b at point (2,3)...

    Text Solution

    |

  9. The ength of substangent to the curve y=e^(x//a) is :

    Text Solution

    |

  10. In the curve x^a y^b=K^(a+b) , prove that the potion of the tangent in...

    Text Solution

    |

  11. Does there exists line/lines which is/are tangent to the curve y=sinx ...

    Text Solution

    |

  12. If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , t...

    Text Solution

    |

  13. The length of normal to the curve x=a(theta+sintheta),y=a(1-costheta) ...

    Text Solution

    |

  14. Determine p such that the length of the sub-tangent and sub-normal is ...

    Text Solution

    |

  15. If f(x)a n dg(x) are continuous functions in [a , b] and are different...

    Text Solution

    |

  16. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

    Text Solution

    |

  17. On the curve x^3=12y the abscissa changes at a faster rate than the or...

    Text Solution

    |

  18. The length x of a rectangle is decreasing at the rate of 5cm/s and the...

    Text Solution

    |

  19. Find the minimum value of (x1-x2)^2+((x1^2)/20-sqrt((17-x2)(x2-13)))^...

    Text Solution

    |

  20. Displacement s of a particle at time t is expressed as s=1/2t^3-6t. Fi...

    Text Solution

    |