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

3 days ago · Both discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. I am quite aware that discrete variables are those values …

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 …

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 …

Nov 14, 2012 · Closure of continuous image of closure Ask Question Asked 13 years ago Modified 13 years ago

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.

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 , …

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...

Jun 6, 2015 · In my mind it seems to say, if a function is continuous, we can show that if it is also differentiable, then it is continuous. Rather than what I was expecting, namely, if a function is …