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 …

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 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.

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?

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

Dec 28, 2015 · Continuous random variables have real numbers as possible values. They are described by their probability density function (pdf). For example, suppose the lifetime X of a light bulb can be …

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

Jan 24, 2015 · A continuously differentiable function f(x) f (x) is a function whose derivative function [Math Processing Error] f (x) is also continuous at the point in question.

Jan 2, 2017 · By definition, a smooth function has a continuous first derivative and a continuous second, third, fourth, etc. all continuous. So a smooth function is also a function with a continuous derivative.

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 …