What is a continuous extension? - Mathematics Stack Exchange
The continuous extension of f(x) f (x) at x= c x = c makes the function continuous at that point. Can you elaborate some more? I wasn't able to find very much on "continuous extension" throughout the web. …
What's the difference between continuous and piecewise continuous ...
Oct 15, 2016 · A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a piecewise continuous
Proof of Continuous compounding formula - Mathematics Stack …
12 Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest rate (as a …
Difference between continuity and uniform continuity
Jan 27, 2014 · To understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function that's continuous on R R but not uniformly continuous on R R.
calculus - Does uniformly continuous functions apply to something like ...
Nov 22, 2025 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant …
Is derivative always continuous? - Mathematics Stack Exchange
Jul 21, 2020 · Is the derivative of a differentiable function always continuous? My intuition goes like this: If we imagine derivative as function which describes slopes of (special) tangent lines to points on a ...
Absolutely continuous functions - Mathematics Stack Exchange
Jan 12, 2015 · This might probably be classed as a soft question. But I would be very interested to know the motivation behind the definition of an absolutely continuous function. To state "A real valued …
Is $\sqrt x$ continuous at $0$? Because it is not defined to the left ...
Sep 5, 2016 · Usually when saying this, textbooks assume the so called infinity type of discontinuity, which apply precisely to points where a function is not defined and tends to infinity. I do understand …
What is the formal definition of a continuous function?
Aug 19, 2022 · The MIT supplementary course notes you linked to give — and use — the following (non-standard) definition: We say a function is continuous if its domain is an interval, and it is continuous …
Continuous functions in Sobolev spaces - Mathematics Stack Exchange
Apr 16, 2023 · Since the Sobolev space only cares about function up to a set of measure zero, we could ask questions about whether functions in the space are continuous, strongly differentiable, etc., but …