I'm trying to understand linear approximation in calculus 3 ( I think). And I need to understand delta epsilon limit definition from calculus 1. I have the equation \[\Delta z = dz + \epsilon _1 \Delta x + \epsilon _2 \Delta y\]
Can anyone help me understand this with pictures or links to helpful sights or anything?
I think I understand some of delta epsilon limit with 1 variable. If you have a domain of \[x-\delta ,x +\delta\] then you have a range of\[[f(x-\delta ,x+\delta]\].

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But I don't exactly know what epsilon is here...|dw:1351625107802:dw|

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