Hi! This is Calculus 3. I'm trying to understand linear approximation (I think). I have to find \[ \Delta z\], and write it in the form \[dz+\epsilon _1\Delta x+\epsilon _2 \Delta y\]. The example problem states that the two epsilons have limits of 0 as \[(\Delta x , \Delta y) \rightarrow (0,0)\]. I would appreciate knowing the significance of this! I have an equation \[z=4x^2y+2x^2\], but any z is fine to work with to demonstrate how stuff works, especially if it makes it simpler!
Any help, even conceptual help not related to any specific problem, would be appreciated!

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I'd also think you'd use the partial derivatives to find out the graph of that plane.

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