[tavilach]

I have my Multivariable Calculus midterm tomorrow, and I don't understand Epsilon-Delta proofs. My TA told me that it probably won't be on the test, but I have a feeling that it will...

Can someone please explain the concept in simple, simple terms?

Thanks .

[SafariX]

epsilon-delta proofs are proofs of limits. You might see something like \lim _{x \rightarrow c} f(x) = L. Now, you want to prove that the limit as x approaches c of the function f is indeed L. You have certain laws and rules that you use for evaluating limits, just like you have different rules for differentiating. But proving limits with delta-epsilon proofs is something like proving derivatives from first principles. I think your understanding of what epsilon and delta represent is wrong. If some function has a limit at some certain point, then you're essentially saying that the closer you get to the point, the closer you'll get to the limit, and that you can get as close to the limit as you want. That's what epsilon is for. For any number greater than zero, epsilon, you can find a value for delta such that all x values near c with maximum distance delta from c is less than epsilon away from L. I'll try to clarify. Say you have the funciton y = x², and you say that the limit as x approaches 2 is 4. Now, let's say I choose epsilon to be 1. That means you have to find a range of x values around 2 such that all the y values are within 1 of 4, or in other words, all the y values are between 3 and 5. If you choose delta to be (2 - sqrt(3)), then all x values within delta of 2, that is, all values from sqrt(3) to 4 - sqrt(3) will have y values that are within epsilon of 4. Epsilon-delta proofs prove that for any arbitrarily small espilon, you can always find some delta such that for all x such that 0 < |x-c| < \delta, f(x) is within espilon of the limit, i.e. |f(x) - L| < \epsilon.

The wonderful world of math. .

[Weezer]

wow, posts at 1:15 am the night before, and gets a detailed nice answer 10 minutes later. Talk about service

[SafariX]

Originally posted by Weezer:
wow, posts at 1:15 am the night before, and gets a detailed nice answer 10 minutes later. Talk about service

I came. I saw. I conq....well mostly I just came.

[Weezer]

Originally posted by SafariX:
I came. I saw. I conq....well mostly I just came.

is that what your girlfriend said???

ooooo

[SafariX]

I didn't even get a thank you?

Tavilach must still dislike me.

[Oneota]

Originally posted by SafariX:
I didn't even get a thank you?

Tavilach must still dislike me.

Probably too busy taking his midterm.