Home
Class 12
MATHS
The temperature in celsius in along rod ...

The temperature in celsius in along rod of length 10m, insulated at both ends , is a function of length x given by `T=x(10-x)`. Prove that the rate of changes of temperature at the midpoint of the rod is zero .

Text Solution

Verified by Experts

The correct Answer is:
`(dT)/(dx)=0`
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

A rod is of length 30m, insulated at both ends. The temperature of the rod is given by T = x (30-x) where x is length. Prove that the rate of change of temperature at the mid point of the rod vanishes.

A rod of length k slides in a vertical plane, its ends touching the coordinate axes. Prove that the locus of the foot of the perpendicular from the origin to the rod is (x^2+y^2)^3=k^2x^2y^2dot

If the volume of a cube of side length x is V = x^(3) . Find the rate of change of the volume with respect to x when x = 5 units.

If the mass m(x) (in kilograms) of a thin rod of length x(in metres) is given by, m(x)=sqrt(3x) then what is the rate of change of mass with respect to the length when it is x = 27 meters.

If the volume of a cube of side length x is v=x^(3) . Find the rate of change of the volume with respect to x when x = 5 units.

If the volume of a cube of side length x is V=x^(3) . Find the rate of change of the volume with respect to x when x = 5 units.

If the mass m(x) (in kilograms) of a thin rod of length x (in meters) is given by, m(x)=sqrt3 x then what is the rate of change of mass with respect to the length when it is x = 3 and x = 27 meters.

FULL MARKS-APPLICATIONS OF DIFFERENTIAL CALCULUS -ADDITIONAL QUESTIONS SOLVED
  1. The temperature in celsius in along rod of length 10m, insulated at bo...

    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

    |