Nov 9, 2024 · I learned a theorem that if $f$ is continuous and bijective then $f^ {-1}$ is continuous. I went online to search for a proof and saw a really long proof in this link.

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 …

Nov 22, 2025 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and …

Apr 25, 2017 · This function is continuous on $ [-1,1]$, so it is uniformly continuous there. A fortiori on $ (-1,1)$.

12 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 …

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") …

Aug 1, 2017 · @user8469759 My goal isn't to prove that x^3 is continuous efficiently, but to prove it using epsilon-delta as practice.

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 but not uniformly …

Oct 29, 2017 · I believe it follows from the fact that we showed $f+g$ is continuous whenever $f$ and $g$ are continuous. Indeed, if $g$ is continuous, then $-g$ is clearly continuous.

Feb 22, 2015 · The projection $ (x,y)\mapsto x$ is a linear transformation and in finite dimensional space $\Bbb R^2$ it's continuous. The same for the second projection and you know the rest …