If z=x^2+y^2, find both dz and delta z, as well as the error that one commits if dz is used instead of delta z.
So far I have dz=2xdx+2ydz.
However, I am not sure how to calculate delta z. Also not sure what the error would be.
Any help would be great, thanks.
Using function notation, Let $f(x,y)=z=x^2+y^2$.
Then $\Delta z=f(x+\Delta x, y+\Delta y)-f(x,y)$.
To compare $dz$ and $\Delta z$, use $dx=\Delta x$ and $dy=\Delta y$.