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$$[f(x-\delta ,x+\delta]$$.

Question

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$$[f(x-\delta ,x+\delta]$$.

theeric · Answer

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