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 …

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

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 …

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 …

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 , …

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 …

Jun 19, 2016 · This would mean that the derivative of a function is always continuous on the domain of the function, but I have encountered counterexamples. I have probably misinterpreted something; …

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 …

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...

I was reading through Munkres' Topology and in the section on Continuous Functions, these three statements came up: If a function is continuous, open, and bijective, it is a homeomorphism. If a