Home
Class 12
MATHS
Use the mean value theorem to prove e^xg...

Use the mean value theorem to prove `e^xgeq1+xAAx in R`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise Exercise 5.1|11 Videos

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise Exercise 5.2|6 Videos

  • 3D COORDINATION SYSTEM

    CENGAGE|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|137 Videos

Similar Questions

Explore conceptually related problems

Use the mean value theorem to prove e^(x)>=1+x AA x in R

Cauchys mean value theorem

Using Lagrange's mean value theorem prove that if b gt a gt 0 "then " (b-a)/(1+b^(2)) lt tan^(-1) b -tan^(-1) a lt (b-a)/(1+a^(2))

Using mean value theorem,prove that tan x>x for all x(0,(pi)/(2))

Using intermediate value theorem,prove that there exists a number x such that x^(2005)+(1)/(1+sin^(2)x)=2005

The value of c in Lagrange's mean value theorem for the function f(x)=log_ex in the interval [1,3] is

A value of c for which the conclusion of mean value theorem holds for the function f(x) = log_(e) x on the interval [1, 3] is:

The value of c in Lagrangel's mean value theorem for the function f(x)=|x| in the interval [-1,1] is

Find 'c' of the mean value theorem, if: f(x) = x(x-1) (x-2), a=0, b=1//2

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

CENGAGE-APPLICATION OF DERIVATIVES-Solved Examples And Exercises
  1. Use the mean value theorem to prove e^xgeq1+xAAx in R

    Text Solution

    |

  2. The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0

    Text Solution

    |

  3. Find the angle of intersection of y=a^xa n dy=b^x

    Text Solution

    |

  4. If the sub-normal at any point on y=a^(1-n)x^n is of constant length,...

    Text Solution

    |

  5. Find the cosine of the angle of intersection of curves f(x)=2^x(log)e ...

    Text Solution

    |

  6. Find the value of a if the curves (x^2)/(a^2)+(y^2)/4=1a n dy^3=16 x c...

    Text Solution

    |

  7. The acute angle between the curves y= |x^2 -1| and y=|x^2- 3| at their...

    Text Solution

    |

  8. In the curve x^(m+n)=a^(m-n)y^(2n) , prove that the m t h power of the...

    Text Solution

    |

  9. Find the length of the tangent for the curve y=x^3+3x^2+4x-1 at point ...

    Text Solution

    |

  10. For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent ...

    Text Solution

    |

  11. For the curve y=f(x) prove that (lenght n or mal)^2/(lenght or tanght...

    Text Solution

    |

  12. Find the condition if the equation 3x^2+4a x+b=0 has at least one root...

    Text Solution

    |

  13. Find c of Lagranges mean value theorem for the function f(x)=3x^2+5x+7...

    Text Solution

    |

  14. Let 0<a<b<pi/2dotIff(x)=|tanxtanatanbsinxsinasinbcosxcosacosb|,t h e n...

    Text Solution

    |

  15. Let f(x)a n dg(x) be differentiable for 0lt=xlt=2 such that f(0)=2,g(0...

    Text Solution

    |

  16. Prove that if 2a0 2<15 a , all roots of x^5-a0x^4+3a x^3+b x^2+c x+d=0...

    Text Solution

    |

  17. If f(x) is continuous in [a , b] and differentiable in (a,b), then pro...

    Text Solution

    |

  18. Prove that |tan^(-1)x-tan^(-1)y|lt=|x-y|AAx , y in Rdot

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |