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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\[[f(x\delta ,x+\delta]\].
 one year ago
 one year ago
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\[[f(x\delta ,x+\delta]\].
 one year ago
 one year ago

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theEricBest ResponseYou've already chosen the best response.0
But I don't exactly know what epsilon is here...dw:1351625107802:dw
 one year ago

theEricBest ResponseYou've already chosen the best response.0
dw:1351625442880:dwHere,\[\Delta y_1 > \Delta y2\]\[\Delta y_1 \ne \Delta y_2\] So the range is not anything like \[[f(x)\epsilon, f(x)+\epsilon]\]
 one year ago

JakeV8Best ResponseYou've already chosen the best response.1
the essence of it is that for some delta surrounding x, the function will be located in some epsilon surrounding f(x). That isn't worded perfectly, but maybe it will help a little. Where this idea is taking you is that you don't want to have to approximate the function with a stairsteplike approach... you would really like to have a way to describe f(x) over a range of x values where you don't have to treat the curve as something like a staircase (imagine a curve pixelated... would look like steps, not smooth).
 one year ago

JakeV8Best ResponseYou've already chosen the best response.1
These videos explain it better than I can :) http://www.khanacademy.org/math/calculus/differentialcalculus/v/epsilondeltalimitdefinition1 http://www.khanacademy.org/math/calculus/differentialcalculus/v/epsilondeltalimitdefinition2
 one year ago

JakeV8Best ResponseYou've already chosen the best response.1
I'm not sure this will help with Calc 3 though :( But it's a good review from Calc 1
 one year ago

theEricBest ResponseYou've already chosen the best response.0
Thank you for your help! :) Not a problem!
 one year ago

JakeV8Best ResponseYou've already chosen the best response.1
sorry, I didn't correctly read your question at first.. missed the fact the variables included z... then I noticed it said Calc 3 :) didn't mean to give you too simplistic a starting point. I do like those videos though :) good luck!
 one year ago

theEricBest ResponseYou've already chosen the best response.0
Thank you! Part of the issue is that I don't think I understand calculus 1 well enough! Lots of things from calculus 1 can be applied to calculus 3. Therefore, I am glad you missed the calculus 3 part :) Take care! And thanks for the video links!
 one year ago

theEricBest ResponseYou've already chosen the best response.0
I learned something... SUCCESS!! :D
 one year ago
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