I was wondering how we could use the limit definition $$ \lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$$ to find the derivative of $e^x$, I get to a point ...

I'm searching for a really simple and beautiful proof that the sequence $(u_n)_{n \in \mathbb{N}} = \sum\nolimits_{k=1}^n \frac{1}{k} - \log(n)$ conv...

I'm teaching our intro to proofs course (well, one of them) and one of the classic illustrations of an overturned "axiom" is the Greek axiom of comme...

Consider a cube whose faces are given by $x+y+z=3\sqrt{3}$, $x+y+z=2\sqrt{3}$, $4x-5y+z=\sqrt{42}$, $4x-5y+z=2\sqrt{42}$, $2x+y-3z=\sqrt{14}$, $2x+y-3z=2\...

Either exhibit 333 different boolean functions on the three variables p; q; r, or prove that there aren’t 333 different such functions $p$ $q$ $r$ $0 0 0$ $...

Cosine is just a change in the argument of sine, and vice versa. $$\sin(x+\pi/2)=\cos(x)$$ $$\cos(x-\pi/2)=\sin(x)$$ So why do we have both of them? Do th...

Consider the heat equation in spherical coordinates (considering only variation in the radial direction): $$\frac{\partial\phi}{\partial t} = \frac{\alpha...

Why does the following statemnet true? $A$ is invertible matrix iff $Ax=0$ has only the trivial solution. My try: Let $x$ a solution of $Ax = 0$. Then, be...

Let's say I want a formula that takes any number and makes it into 170, and I come up with a formula that I think does it. If I plug 1 into it, 2 int...

Okay, I know what you're thinking : this question has been asked a billion times before. But I have done my research, and sadly, the only answers I h...