If the continuous function \(z = f(x, y)\) is given by: \(\lim\limits_{(x,y) \to (a,b)} \frac{f(x,y) - (cx + ey + g)}{\sqrt{(x-g)^2 + y^2}} = j\) where \(a, b, c, e, g, j\) are constants, then the function can be expressed as \(f(x, y) = cx + ey + g + o(\rho),\)
where \(\rho = \sqrt{(x-g)^2 + y^2}\), and at the point \((a, b)\), we have:
$\left .dz \right| _{(a,b)}=cdx + edy$
a multivariable countinous function and derivation
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