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I just have a question regarding "estimating" the value of a function at a given point. Say we have a function [itex]f(x, y, z, w)[/itex] and we want to know the value of that function at [itex]f(1.99, 1.001, 8.02, 2.01)[/itex]

Can we simply do the following:

let [itex]f=f(2, 1, 8, 2)[/itex] and

[itex]df=\frac{\delta f}{\delta x}dx+\frac{\delta f}{\delta y}dy+\frac{\delta f}{\delta z}dz+\frac{\delta f}{\delta w}dw[/itex]

Then say:

[itex]f(1.99, 1.001, 8.02, 2.01)=f(2, 1, 8, 2)(1-df)[/itex]

??? or is that completely wrong?

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# Homework Help: Using differential nad linear approximation

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