ε / δ question (HELP!)?
I've been given a question but I have absolutely no idea what these two symbols even mean. I only know they're related to limits.
The question asks me to explain this following definition and how it relates to computing limits:
lim f(x) = L
x->a
for any ε >0 there exists a δ < 0 such that if
0 < |x-a| < δ , then | f(x) - L| < ε
any help would be appreciated!
More Questions From This User See All
Answers & Comments
Verified answer
First of all the "delta" should be greater than 0, not less than 0. Delta and epsilon represent real numbers.
0 < |x-a| < d means that x is close to the point a (within d units in fact), the fact that it's greater than 0 here just means that x doesn't equal a.
|f(x) - L| < e says that f(x) (the y-value at the same point x) is close to the y-value L (within e units).
This statement says that no matter what e you pick, no matter HOW SMALL, we will be able to find a little area around x (on the x-axis) where the y-values of f will be really close to L for all values of f on that little area around x.
This area around x is described with d. If f is continuous at x, we will be able to find a d small enough that the y-values of f(x) will be really close to L (within e) for all numbers within d units of x on the x-axis.
(Sorry I used d an e instead of delta and epsilon. I'm not sure how to get the Greek symbols. I hope it's clear.)