Prove that $$\int^{1}_{0} \sqrt{x}\sqrt{1-x}\,dx = \frac{\pi}{8}$$ $$\textit{proof}$$ Consider the function $$f(z) = \sqrt{z-z^2} = e^{\frac{1}{2}\log(z-z...

I've noticed that a lot of the derivations for the cubic and quartic polynomial solutions require you to depress them, but what about in a case by ca...

In the lambda expression (λx. (λy. y z)(λw. w) z x)[z→y], I'm inclined to change y to another variable, then perform the substitu...

For $$e^{-j\pi n}$$ How does this become $$(-1)^n$$ or is it actually $$(-1)^{-n}$$ I have checked on calculator and values are all the same when the same...

Is there a proper notation for denoting subspaces? For example, if $U$ is a subspace of some vector space $V$. I would usually just write "the subspace $U...

I am looking for a proof using the min-max principle. Wikipedia seem to provide just that: http://en.wikipedia.org/wiki/Min-max_theorem#Cauchy_interlacing...

What is the difference between local and global differential geometry? I cannot find their (exact) definitions. There are some other terms in geometry lik...

Okay, I know that this question is probably somewhere on this site. But I couldn't find it after looking for over an hour so I'm just going to p...

I had a question that goes like this: Let $m$ be the number of local minima and $M$ be the number of local maxima. Can you create a function where $M >...

so I have been working on limits and I thought I understood it, but my online homework says I have been incorrect. What am I doing wrong? Could someone ex...