7
votes
1answer
175 views

A functional relation which is satisfied by $\cos x$ and $\sin x$

Assume that the functions $f,g : \mathbb R\to \mathbb R$ satisfy the relations \begin{align} \left\{ \begin{array}{ll} f(x+y) &=& f(x)f(y)-g(x)g(y), \\ g(x+y) &=& f(x)g(y)+f(y)g(x), ...
2
votes
0answers
54 views

Symmetry between differentiation and integration [duplicate]

I want to make clear, that I am interested in the question: Why does integration need a bigger spectrum of functions than differentiation and not why integration is harder!!! as experience told me, ...
0
votes
3answers
524 views

Intersection of chord with circle knowing the length and a point

Let's take a circle with radius R, and center in O (0, 0). We take on this circle a point A with coordinates xA and yA. We know that point A is one of the endings of a chord with length l. Which is ...
0
votes
3answers
121 views

Given $n+1\mid2\sum_{k=1}^{n}{a_k}$, find $a_k$.

Let $m$ be a positive integer. There are only 2 finite sequences of positive integers like $a_1,a_2,...,a_m$ such that $$(\forall n \leq m)\left(n+1\mid2\sum_{k=1}^{n}{a_k}, \quad a_n\in [1,m],\quad ...
4
votes
0answers
269 views

“Green Globs” question

When I was in high school geometry, we had a fun little game on the computer called Green Globs (the website for the software is http://www.greenglobs.net/index.html). A number of targets (globs) are ...
7
votes
5answers
231 views

Understanding analysis/integration properties over $[0,1]$ and $[0,\infty)$ from an algebraic perspective?

I've noticed that in analysis we often treat the unit-interval $[0,1]$ differently from $[0,\infty)$, particularly in improper-integration (but certainly not limited to). By lieu of example, ...