epsilon delta... wah?

tehbribe · New Member Offline Joined: 19 Sep 2005 Posts: 2

hi,

i took calc in high school and now i am retaking it again as a prereq for college and i am finding out very quickly that i have been taught cookbook calculus Sad

so, basically i've been doing the homework using what i know... but i really do want to learn the "real" way to go about solving a problem... but i dunno if its the way my professor explained it or what, but i simply don't get the relation between epsilon and delta and how they are applied to limiits and how they are applied thoughout calculus..

i've poured through the previous pages here and didn't find an answer, so now i am forced to pose this thread at the risk of looking like an idiot Sad

thanks in advance
tb

**Posted:** Mon Sep 19, 2005 9:44 pm

Kent Merryfield

There's no way I could teach you this in a few on-line posts. Talk to your instructor, or get help from someone else who knows what he's doing.

I do have one insight to offer. Let's look at that definition again:

$\lim_{x\to a}f(x)=L\iff\,\forall\,\epsilon>0,\,\exists\,\delta>0$ such that if $x$ is in the domain of $f$ and $0<|x-a|<\delta,$ then $|f(x)-L|<\epsilon.$

Note that to use this definition, you must already know $L.$ In other words, this, the official definition of limit, cannot itself be used to find an unknown limit. It's not a technique for finding limits; it is a standard of proof. You use it to verify a number of useful theorems: the limit of a sum is the sum of the limits (provided both exist); the limit of a product is the product of the limits (provided both exist); the limit of a quotient is the quotient of the limits, provied both exist and the denominator limit is not zero; the squeeze theorem; the composition of continuous functions is continuous. And those theorems are what you use in practice to find limits.

**Posted:** Tue Sep 20, 2005 5:19 pm

tehbribe · New Member Offline Joined: 19 Sep 2005 Posts: 2

so as it pertains to limits, epsilon and delta are just variables(essentially) that are used to represent arbitrary values that exist near the point of c????

I've talked to him and he offers up the same stuff he threw out in class Mad

so it's not a way to solve limit equations then, just to prove the theorums that are used to solve limits....

so, if i may(i'm probably getting ahead of myself, but i'll ask anyway), how are these applied to computer science and such?

and, sorry for this last question, but im reading more as im typing... but is one supposed to be looking for a coorelation b/w |f(x) - L| and |x-c| ??? or something else....

sorry for the randomness.... i'll try talking to my instructor again, hopefully i can force him to explain this to a point where i get it...

thanks for the insight and any further insight,
tb

**Posted:** Wed Sep 21, 2005 2:25 pm