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" throughout the web. …

Dec 14, 2025 · 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 …

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 R R but not uniformly continuous on R R.

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? Is …

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

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?

Jan 24, 2015 · Note the ending "-ly", which makes it an adverb, not an adjective. So "continuously differentiable" means "differentiable in a continuous way".

I know that the image of a continuous function is bounded, but I'm having trouble when it comes to prove this for vectorial functions. If somebody could help me with a step-to-step proof, that would be great.

I think you mean a ≠ 0 a≠0. As you have it written now, you still have to show √x x−−√ is continuous on [0, a) [0,a), but you are on the right track. As @user40615 alludes to above, showing the function is …