Home
Class 12
MATHS
Prove , using mean value theorem, that |...

Prove , using mean value theorem, that `|sin alpha -sin beta | le| alpha-beta|, alpha, beta in RR`.

Text Solution

Verified by Experts

The correct Answer is:
`|sin alpha -sin beta| le| alpha -beta|.`
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DIFFERENTIAL CALCULUS

    FULL MARKS|Exercise EXERCISE - 7.1|10 Videos
  • APPLICATIONS OF DIFFERENTIAL CALCULUS

    FULL MARKS|Exercise EXERCISE - 7.2|10 Videos
  • APPLICATIONS OF INTEGRATION

    FULL MARKS|Exercise ADDITIONAL PROBLEMS|35 Videos

Similar Questions

Explore conceptually related problems

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

alpha beta x ^(alpha-1) e^(-beta x ^(alpha))

By vector method, Prove that sin(alpha-beta)=sinalphacosbeta-cosalphasinbeta

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

Prove by vector method that sin(alpha+beta)=sinalphacosbeta+cosalphasinbeta.

Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) ]:} =0

The minimum value of the expression sin alpha + sin beta+ sin gamma , where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that sin 3alpha + sin 3 beta + sin 3gamma = 3 sin (alpha + beta + gamma)

IF alpha , beta and gamma are angles such that tan alpha + tan beta + tan gamma = tan alpha tan beta tan gamma and x= cos alpha + i sin alpha , y = cos beta + i sin beta and z= cos gamma + i sin gamma , then xyz =

By geometrical interpretation, prove that (i) sin(alpha+beta)=sin alpha cos beta+sinbeta cosalpha (ii) cos(alpha+beta)=cosalpha cosbeta -sin alpha sinbeta

FULL MARKS-APPLICATIONS OF DIFFERENTIAL CALCULUS -ADDITIONAL QUESTIONS SOLVED
  1. Prove , using mean value theorem, that |sin alpha -sin beta | le| alph...

    Text Solution

    |

  2. A water tank has the shape of an invertd circular cone with base radiu...

    Text Solution

    |

  3. A car A is travelling from west at 50 km/hr and car B is travelling to...

    Text Solution

    |

  4. The distance x metres travelled by a vehicle in time t seconds after t...

    Text Solution

    |

  5. At a particular instant ship A is 100 km west of ship B, ship A is sai...

    Text Solution

    |

  6. Gravel is being duped from a conveyor belt at a rate of 30 ft^(3)//min...

    Text Solution

    |

  7. Prove that the sum of the intercepts on the co-ordinate axes of any ta...

    Text Solution

    |

  8. Find the equation of normal to y = x^(3) -3x that is parallel to 2x + ...

    Text Solution

    |

  9. Prove that the curves 2x^(2)+4y^(2)=1 and 6x^(2)-12y^(2)=1 cut each ot...

    Text Solution

    |

  10. Show that the equation of the normal to the curve x=a cos ^(3) theta, ...

    Text Solution

    |

  11. If the curve y^(2) = x and xy = k are orthogonal then prove that 8k^(2...

    Text Solution

    |

  12. Verify Rolle's theorem for the following f(x) = x^(3) -3x + 3 " in "...

    Text Solution

    |

  13. Suppose that f(0) = -3, and f' (x) le 5 for all values of x how large ...

    Text Solution

    |

  14. Using Rolle's theorem find the point on the curve y=x^(2)+1,-2lexle2 w...

    Text Solution

    |

  15. Find 'C' of Lagrange's mean value theorem for the function f(x)=2x^(3)...

    Text Solution

    |

  16. Find 'C' of Lagrange's mean value theorem for the function f(x) =x^(3)...

    Text Solution

    |

  17. The Taylor's series expension of f(x)=sin x "about" x=(pi)/(2) is obta...

    Text Solution

    |

  18. Obatin the Maclaurin's series expansion for the following function . ...

    Text Solution

    |

  19. Evaluate underset(x rarr (pi)/(2))(lim) (log sin x)/((pi - 2x)^(2))

    Text Solution

    |

  20. Evaluate: underset (xrarr0) lim (cot x) ^(sin x)

    Text Solution

    |

  21. underset (x rarr infty) lim(log x^(x))/(x)

    Text Solution

    |