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" …

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 …

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 …

May 10, 2019 · This function is always right-continuous. That is, for each x ∈ Rk x ∈ R k we have lima↓xFX(a) =FX(x) lim a ↓ x F X (a) = F X (x). My question is: Why is this property important? …

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 …

Nov 18, 2015 · Then f f is continuous if and only if f(A¯¯¯¯) ⊆f(A)¯ ¯¯¯¯¯¯¯¯¯ f (A) ⊆ f (A), where A¯¯¯¯ A denotes the closure of an arbitrary set A A. Assuming f f is continuous, the result 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?

May 7, 2016 · A constant function is continuous, but for most topologies does not map an open set to an open set. For a familiar somewhat different example, the image of (0, 42) (0, 42) …

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]$ …

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 …