Home
Class 12
MATHS
Using Lagranges mean value theorem, prov...

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

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

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

Using Largrange's mean value theorem, prove that, tan^(-1)x lt x

State Lagrange's mean value theorem.

Using Lagrange's mean value theorem prove that, (b-a)sec^(2)a lt tan b-tan a lt (b-a)sec^(2)b when 0 lt a lt b lt (pi)/(2) .

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

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

Using Lagrange's mean value theorem show that, (b-a)/(b) lt "log"(b)/(a) lt (b-a)/(a) , where 0 lt a lt b .

Using Lagrange's mean value theorem, find a point on the curve y=sqrt(x-2) defined in the interval [2, 3] where the tangent to the curve is parallel to the chord joining the end points of the curve.

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Let f(x)a n dg(x) be two differentiable functions in R a n d f(2)=8,g(...

    Text Solution

    |

  2. Discuss the extremum of f(x)={x^2+x^-2}

    Text Solution

    |

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

    Text Solution

    |

  4. Find the maximum value and the minimum value of 3x^4-8x^3+12 x^2-48 x+...

    Text Solution

    |

  5. Find the value of the x^2+7xy+y^2, when x=-2, y=-5

    Text Solution

    |

  6. Discuss the global maxima and global minima of f(x)=tan^(-1) x- (log)e...

    Text Solution

    |

  7. Suppose alpha,beta a n d theta are angles satisfying 0 < alpha < thet...

    Text Solution

    |

  8. Find the range of the function f(x)=2sqrt(x-2)+sqrt(4-x)

    Text Solution

    |

  9. Let f be continuous on [a , b],a >0,a n d differentiable on (a , b)dot...

    Text Solution

    |

  10. Discuss the extremum of f(x)=2x^3-3x^2-12 x+5 for x in [-2,4] and the ...

    Text Solution

    |

  11. Two men Pa n dQ start with velocity u at the same time from the juncti...

    Text Solution

    |

  12. Discuss the extremum of f(x)=1+2sinx+3 cos^2x ,0lt=xlt=(2pi)/3

    Text Solution

    |

  13. x and y are the sides of two squares such that y=x-x^2 Find the rate o...

    Text Solution

    |

  14. Discuss the extremum of f(x)=sinx+1/2sin2x+1/3sin3x ,0lt=xlt=pidot

    Text Solution

    |

  15. A spherical iron ball 10 cm in radius is coated with a layer of ice of...

    Text Solution

    |

  16. How many roots of the equation 3x^(4) + 6x^(3) + x^(2) + 6x + 3 = 0 ar...

    Text Solution

    |

  17. Two cyclists start from the junction of two perpendicular roads, there...

    Text Solution

    |

  18. Let f(x)=-sin^3x+3sin^2x+5 on [0,pi/2] . Find the local maximum and ...

    Text Solution

    |

  19. Tangent of an angle increases four times as the angle itself. At what ...

    Text Solution

    |

  20. Discuss the extremum of f(x)=1/3(x+1/x)

    Text Solution

    |