# Error analysis

• Jun 7th 2010, 01:44 AM
bobred
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
• Jun 8th 2010, 03:21 AM
CaptainBlack
Quote:

Originally Posted by bobred
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
• Jun 8th 2010, 03:34 AM
bobred
I thought so, thanks

James