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Math Help - Total Differential

  1. #1
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    Total Differential

    Hello ! Im just diving into multi-variable Calculus and having some problems. Currently im trying to solve this:


    Approximate by using the total differential how the surface of a cylinder with soil and lid is changing if its radius = 10cm is increased by 5% and its height = 25cm is decreased by 2%. Compare this to the exact result and explain

    any ideas ? especially how to get into this in general

    thank you
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  2. #2
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    Quote Originally Posted by coobe View Post
    Hello ! Im just diving into multi-variable Calculus and having some problems. Currently im trying to solve this:


    Approximate by using the total differential how the surface of a cylinder with soil and lid is changing if its radius = 10cm is increased by 5% and its height = 25cm is decreased by 2%. Compare this to the exact result and explain

    any ideas ? especially how to get into this in general

    thank you
    1. Your function describes the volume of a cylinder with respect to r and h:

    v(r,h)=\pi r^2 \cdot h

    2. I assume that you know that the total differential of a function z(x,y) is calculated by:

    dz = \frac{\partial z}{\partial x}\cdot dx  + \frac{\partial z}{\partial y}\cdot dy

    3. In your case:

    dv = \frac{\partial v}{\partial r}\cdot dr  + \frac{\partial v}{\partial h}\cdot dh

    4. You know the values of r and dr = 0.5
    and h and dh = 0.5

    Plug in the known values and calculate dv.
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