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I was asked this on exam today:

f(1,2)=8, f(1.01,2)=8.4, f(1,2.01)=7.8, f(1.01,2.01)=8.3 x=1±0.02, y=2±0.03

What is the limit of error in f?

I believe it should be the error propagation formula so I should use the data to approixate the derivate. Correct? But how do I approximate the derivates and is that the right way to go?

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The first order partials can be approximated using the values of $f$, for example $f_x(1,2)\approx (8.4-8)/0.01= 40$. Similarly, $f_y(1,2)$ appears to be around $-20$. However, I never heard of the error propagation formula - could you add it to your question? – user31373 Sep 24 '12 at 6:32

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