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Math Help - Using differentials to estimate a maximum error

  1. #1
    MHF Contributor arbolis's Avatar
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    Using differentials to estimate a maximum error

    Four positive numbers lesser than 50 each are rounded to the first decimal and then multiplied between themselves. Use differentials to estimate the maximum possible error of the product.
    My attempt : Let x, y and z be the 3 numbers.
    We have (x+\Delta x)(y+\Delta y)(z+\Delta z)=0.1(zx+zy+xy)+0.01(z+x+y)+0.001.
    Note that I considered \Delta x = \Delta y = \Delta z =0.1.
    However I don't see how I can use differentials. I don't see any way to involve them. So I didn't solve the problem...
    Do you have any idea?
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  2. #2
    Super Member malaygoel's Avatar
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    If P is the product and x,y,z are numbers, then

    P=xyz

    hence, we have,
    dP=yzdx + xzdy + xydz

    For maximum possible error, dx, dy and dz are maximum.


    -----------------------------------------------------------------
    You have used

    <br />
\Delta x = \Delta y = \Delta z =0.1<br />

    It cant be >0.5
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  3. #3
    MHF Contributor arbolis's Avatar
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    Ok you've done dP=\frac{\partial P}{\partial x}+\frac{\partial P}{\partial y}+\frac{\partial P}{\partial z}.
    But then you wrote
    For maximum possible error, dx, dy and dz are maximum.
    but these are differentials. I don't see how dx, dy and dz can have a maximum value if any numerical given value.
    -----------------------

    You have used



    It cant be >0.5
    Ok, so I'm correct then?
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