1. ## 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

2. 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

3. I thought so, thanks

James