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") …

2016年10月15日 · 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 …

2019年5月10日 · 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 …

2014年1月27日 · 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 …

2012年1月13日 · 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?

2015年1月24日 · 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 …

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, …

A function f: [0, 1] → R f: [0, 1] → R is called singular continuous, if it is nonconstant, nondecreasing, continuous and f′(t) = 0 f (t) = 0 whereever the derivative exists. Let f f be a …