Recent content by Fire flame

So I understand why there isn't an f(a) since the derivative of a constant is zero, but like in my problem one of my limits is zero and since the function isn't given it could be anything, even something like f(x) = 1/x which at zero is undefined, but in my problem it just goes away to zero...

I'm in analysis and I'm trying to understand the following. Homework Statement g(x) = integral from 0 to x+δ of f(x)dx + integral from x-δ to 0 of f(x)dx g'(x) = f(x+δ) - f(x -δ) So how do they get g'(x)?

Actually now that I'm looking at my professors notes more I do see that he indeed labeled δ1 and δ2 separately even though they are in the end the same. So is there anything else wrong with my write up? I just turned in the homework yesterday and I will see what I get on this problem.

I'm going to take a few guesses. 1. What if both f and g are the same function then they would have the same δ and ε values. 2. Because they are both uniformly continuous. 3. Because I am picking the same ε for each function. I have tried to understand the whole ε δ thing many times...

Can't you just choose what ε and δ is? It can have many values as long as its > 0. Right?

Homework Statement Let f, g : D→R be uniformly continuous. Prove that f-g: D→R is uniformly continuous aswell Homework Equations none The Attempt at a Solution Okay, I am posting this question because I want to make sure that my solution is correct and if it isn't I would...

Definition: Let S be a subset of R. A point x in R is an accumulation point of S if every deleted neighborhood of x contains a point of S. So this is what I get out of it. Lets say S is a subset of R and S is the interval [0,1) So basically, you take a point, any point x in R and then...

I don't know what an accumulation point is and I have read the definition many many times. Could someone please give me a few examples with intervals of what would be an accumulation point? Thank you!