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 …
calculus - Why exactly does a function need to be continuous on a ...
Dec 11, 2015 · If the function is not continuous at the end points then its value at the endpoints need have nothing to do with the values the function takes on the interior of the interval. If you did want to …
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 but not uniformly continuous on R.
probability theory - Why does a C.D.F need to be right-continuous ...
May 10, 2019 · Of course, the CDF of the always-zero random variable $0$ is the right-continuous unit step function, which differs from the above function only at the point of discontinuity at $x=0$.
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 …
Are there any functions that are (always) continuous yet not ...
Are there any examples of functions that are continuous, yet not differentiable? The other way around seems a bit simpler -- a differentiable function is obviously always going to be continuous.
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 ...
calculus - Relation between differentiable,continuous and integrable ...
The containment "continuous"$\subset$"integrable" depends on the domain of integration: It is true if the domain is closed and bounded (a closed interval), false for open intervals, and for unbounded intervals.