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 …

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 …

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 $x=0$.

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 …

Jul 14, 2018 · You are confusing "piecewise" with "step". The absolute value function has a piecewise definition, but as you and the text correctly observe, it is continuous. Informally, the pieces touch at …

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 …

Consider a function f(x) f (x) that has no jump, infinite, or removable discontinuities in the middle anywhere -- but maybe the domain is limited: Would the endpoint [a, [a, be considered continuous? …

Dec 28, 2015 · Typically the range of a continuous random variable is $\mathbb {R}$, $ [0,\infty)$, or some interval $ [a,b]$. Examples of continuous random distributions are the normal distribution, chi …

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...