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 2 years 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\[[f(x\delta ,x+\delta]\].
 2 years 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\[[f(x\delta ,x+\delta]\].

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theEric
 2 years ago
Best ResponseYou've already chosen the best response.0But I don't exactly know what epsilon is here...dw:1351625107802:dw

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

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1the 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).

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1These 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

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1I'm not sure this will help with Calc 3 though :( But it's a good review from Calc 1

theEric
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you for your help! :) Not a problem!

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1sorry, 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!

theEric
 2 years ago
Best ResponseYou've already chosen the best response.0Thank 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!

theEric
 2 years ago
Best ResponseYou've already chosen the best response.0I learned something... SUCCESS!! :D
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