My book gives a formula for linear approximation of two independent variables, but I needed one for three. So I modified the formula given in the book, but I need someone to please just quickly see if it looks okay.(adsbygoogle = window.adsbygoogle || []).push({});

Given:

[tex]f(x,y)=z=f(x_0,y_0)+(\frac{\partial f}{\partial x} (x_0,y_0)) (x-x_0) + (\frac{\partial f}{\partial y} (x_0,y_0)) (y-y_0)[/tex]

Modified:

[tex]f(x,y,z)=f(x_0,y_0,z_0)+(\frac{\partial f}{\partial x} (x_0,y_0,z_0)) (x-x_0) + (\frac{\partial f}{\partial y} (x_0,y_0,z_0)) (y-y_0)+(\frac{\partial f}{\partial z} (x_0,y_0,z_0)) (z-z_0)[/tex]

Does this look alright?

It looks fine to me but I'm prone to overlooking glaring errors :grumpy:

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# Linear Approximation

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