## theEric 3 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$[f(x-\delta ,x+\delta]$.

1. theEric

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

2. theEric

|dw:1351625442880:dw|Here,$\Delta y_1 > \Delta y2$$\Delta y_1 \ne \Delta y_2$ So the range is not anything like $[f(x)-\epsilon, f(x)+\epsilon]$

3. JakeV8

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 stairstep-like 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).

4. JakeV8
5. theEric

|dw:1351626048536:dw|

6. JakeV8

I'm not sure this will help with Calc 3 though :( But it's a good review from Calc 1

7. theEric

Thank you for your help! :) Not a problem!

8. JakeV8

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!

9. theEric

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!

10. theEric

I learned something... SUCCESS!! :D