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

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 $x=0$.

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 …

What is the difference between continuous derivative and derivative? According to my teacher's solution to the assignment, it seems there exits a difference between continuous derivative and derivative.

Jan 13, 2012 · the difference is in definitions, so you may want to find an example what the function is continuous in each argument but not jointly

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 …

In general, is a bounded linear operator necessarily continuous (I guess the answer is no, but what would be a counter example?) Are things in Banach spaces always continuous?

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 …

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