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Math Help - Error analysis

  1. #1
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    Error analysis

    Hi

    Not sure if this is in the right section, if not could someone suggest a better one?

    I am given the function below and told that x=3 and y=-5 with a tolerance of \pm0.02 and \pm0.03 respectively.

    f(x,y)=x^{3}+x^{2}y+y^{2}+2y

    I am asked to find the accuracy of f(x,y), I have

    \frac{\partial f}{\partial x}=3x^{2}+2xy and \frac{\partial f}{\partial y}=x^{2}+2y+2 using the formula \delta f=\frac{\partial f}{\partial x}\delta x + \frac{\partial f}{\partial y}\delta y, my question is what value do I use for \delta x, \delta y, do I use 0.02 and 0.03 or do I use 0.04 and 0.06?

    Thanks James
    Last edited by bobred; June 8th 2010 at 12:21 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bobred View Post
    Hi

    Not sure if this is in the right section, if not could someone suggest a better one?

    I am given the function below and told that x=3 and y=-5 with a tolerance of \pm0.02 and \pm0.03 respectively.

    f(x,y)=x^{3}+x^{2}y+y^{2}+2y

    I am asked to find the accuracy of f(x,y), I have

    \frac{\partial f}{\partial x}=3x^{2}+2xy and \frac{\partial f}{\partial y}=x^{2}+2y+2 using the formula \delta f=\frac{\partial f}{\partial x}\delta x + \frac{\partial f}{\partial y}\delta y, my question is what value do I use for \delta x, \delta y, do I use 0.02 and 0.03 or do I use 0.04 and 0.06?

    Thanks James
    The top end of the interval is obtained by choosing \delta x=\pm0.02 and \delta y=\pm0.03 which gives the largest value of \delta f, and similarly for the bottom end of the interval. Which you choose depend on the signs of the partial derivatives at the point in question.

    which in practice will reduce to:

    \delta f=\pm \left( \left| \frac{\partial f}{\partial x}\right|0.02+\left|\frac{\partial f}{\partial y} \right|0.03\right)

    CB
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  3. #3
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    I thought so, thanks

    James
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