Proof that $a_n < b_n \implies \lim(a_n) \le \lim(b_n)$
First of all, I'm aware that there are many questions like this on the site, but they all seem to be related to either $\limsup$ or $\liminf$ and I c...
Category: General
Why is it that Runge's phenomenon gives rise to oscillations at the edges and not in other locations?
Why is it that Runge's phenomenon gives rise to oscillations at the edges and not in other locations? What I don't understand is why the oscilla...
Law of Sines will give a unique solution iff a > b?
Given a triangle ABC, with known sides a=BC and b=AC, and known angle A, we wish to find angle B. This is a typical application of the Sine Rule (Law of S...
Proving the Secant Angles in the Circle
Ok, I know this is a very easy circle geometry problem, but I want to know that how to prove the theorem of angles in the circle. Like this image here: Ho...
Geometric intepretation of Holder continuous functions?
I've started working with Holder spaces recently and I'm wondering how I should think of them intuitively? I really have no idea what a function...
A typical example of Homeomorphism
The set $\mathbb{R}^2-\{(0,0)\}$ with the usual topology is: (A) Homeomorphic to the open unit disc in $\mathbb{R}^2$ (B) the cylinder $\{(x,y,z)\in \math...
Find the value of A, B and C in the identities.
$6x^3 -11x^2 + 6x + 5 \equiv (Ax-1)(Bx - 1)(x - 1) + c$ Find the value of A, B and C. I started it like this: $6x^3 -11x^2 + 6x + 5 \equiv (Ax-1)(Bx - 1)(...
Find basis of 4x3 Matrix
I've been confused with the following matrix. I'm trying to find the basis of the image of A: $$A= \left( \begin{array}{ccc} 6&4&10\\ 4&...
Probability of getting two pair in poker
I was looking at this website http://www.cwu.edu/~glasbys/POKER.HTM and I read the explanation for how to calculate the probability of getting a full hous...
A generalization of the Euler Line
Today, we had a lecture on Euler line and it's various generalizations/applications. One of the tasks we were given as homework is the following one:...
