What is a continuous extension? - Mathematics Stack Exchange
To find examples and explanations on the internet at the elementary calculus level, try googling the phrase "continuous extension" (or variations of it, such as "extension by continuity") simultaneously …
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 …
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 …
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 $\mathbb R$ but not uniformly …
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 …
calculus - Is a differentiable function always continuous ...
Sep 14, 2014 · 9 Continuous Functions are not Always Differentiable. But can we safely say that if a function f (x) is differentiable within range $ (a,b)$ then it is continuous in the interval $ [a,b]$ . If so , …
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 …
Continuous versus differentiable - Mathematics Stack Exchange
A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...