I recently read about superperfect numbers: $σ^2(n) = 2n$, where $σ(n)$ is the divisor function. I saw that the first few numbers were: $2, 4, 16, 64, 409...

So I'm trying to solve this problem: Take the derivative of $2^{t^{3}}$ This is the relevant text from my textbook which makes sense to me. The trick...

I'm a beginner student study the proof of sum and difference trigonometry formula. There is a formula that: $$\cos(\alpha-\beta) = \cos(\alpha)\cos(\...

I thought you have to say a mapping is onto something... like, you don't say, "the book is on the top of"... Our book starts out by saying "a mapping...

I'm going through my first year of teaching AP Calculus. One of the things I like to do is to impress upon my students why the topics I introduce are...

When I was in lower school I remember playing the Four $4$'s game and we got to around $10$. For those of you who don't know the Four $4$'s...

I think I don't understand how it works.. I found some proofs.. okay, let's see: Well I'd like to show that the function, $$f(x) = \begin{c...

As stated on the title, my question is: (a) represent the function $ f(x) = 1/x $ as a power series around $ x = 1 $. (b) represent the function $ f(x) = ...

If $R = \{(1,2)(1,1),(1,3),(3,2),(2,3)\}$ what is the domain and codomain of $R$? In class, the professor did not give a clear definition and straight-for...

I'm looking for a concave down increasing-function, see the image in the right lower corner. Basically I need a function f(x) which will rise slower ...