Home
Class 12
MATHS
Using lagrange's mean value theorem, sho...

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

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

If vec(alpha) and vec (beta) are perpendicular to each other , show that | vec(alpha) + vec(beta)|^(2) = |vec(alpha)-vec(beta)|^(2)

If alpha and beta are complementary angles, then show that cot beta+cos beta= (cos beta)/(cos alpha) (1+sin beta) .

If sin 2 alpha = 4 sin 2 beta, "show that", 5tan ( alpha -beta) = 3 tan ( alpha +beta)

If alpha and beta are the complex cube roots of 1 show that, alpha^(4)+beta^(4)+alpha^(-1).beta^(-1)=0.

If tan beta = (n sin alpha cos alpha)/(1-n sin^(2) alpha), "show that", tan (alpha - beta) = (1 - n) tan alpha.

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta -alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If cos beta is the geometric mean of sin alpha and cos alpha, then show that cos 2 beta= -2 cos^(2) ((pi)/(4)+alpha)

If alpha,beta,gamma are real numbers, then without expanding at any stage, show that |1cos(beta-alpha)"cos"(gamma-alpha)"cos"(alpha-beta)1"cos"(gamma-beta)"cos"(alpha-gamma)"cos"(beta-gamma)1|=0

If tan alpha = (x sin beta)/(1-x cos beta) " and " tan beta = (y sin alpha)/(1-y cos alpha),"show that", (sin alpha)/(sin beta) = x/y .

If sin alpha sin beta - cos alpha cos beta + 1 = 0,"show that", sin (alpha + beta) = 0, "hence deduce that," 1 + cot alpha tan beta = 0.

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Consider the function f(x)=8x^2-7x+5 on the interval [-6,6] .the valu...

    Text Solution

    |

  2. Let f(x)={x^3-x^2+10 x-5,xlt=1, \ -2x+(log)2(b^2-2),x >1 Find the val...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the minimum value of |x-1|+|x-2|+|x-3|

    Text Solution

    |

  5. Let f(x)a n dg(x) be two differentiable functions in R a n d f(2)=8,g(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |