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

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.

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 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.

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.

Dec 26, 2025 · Let (X, n) (X, n) be normed space and B B a basis (by basis I mean a set of vector such that every vector in X can be expressed in an essentially unique way as a finite linear combination of …

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 …

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

Oct 28, 2024 · Integral of non-continuous function Ask Question Asked 1 year, 2 months ago Modified 1 year, 2 months ago