So after watching the famous video on youtube How to turn a sphere inside out I noticed that the sphere is deformed into 8 bulges in the process. Is there...

I've seen multiple solutions to this well-known problem (posed, among other sites, at http://thinkzone.wlonk.com/MathFun/Triangle.htm). None of the s...

For eigenvalue 1, the eigenspace I got was $span[ 1,0,0]$, and for eigenvalue 4, the eigenspace I got was $span[ 1,-3,9]$. Do they look right? The reason ...

I want to show that $f(x) = x \sin(\frac{1}{\sqrt{x}})$ , with $f(0)=0$ on $[0,1]$ is of bounded variation. To do that I Don't want to use of showing...

$$\int \frac{x\ln\left(x+\sqrt{x^{2}+1}\right)}{\sqrt{x^{2}+1}}dx$$ I honestly have been struggling with this integral for 2 hours straight and none of my...

When I apply the root test to power series I know that $$R= \frac{1}{\limsup_{n\rightarrow\infty}{\sqrt[n]{|c_n|}}}$$ So if I get $1$ as the result of the...

Given $|z^4 -8 + 3|, |z|=2 $ I need to find the positive upper and lower bounds of the above expression. My attempt: By triangle inequality, we have $||z^...

This goes without saying, but, I can't use a calculator to evaluate $\pi^\pi$. I think we need to find a integer $x$ such that $$x<\pi^\pi < x+...

I am asked to the find the value $c$ such that the system has a solution other than $(0, 0, 0)$. This is the linear system: \begin{array}{rcrcrcl} cx &...

As the title indicates, I'm curious why direct proofs are often more preferable than indirect proofs. I can see the appeal of a direct proof, for it ...