$$\lim_{x\to0^+}\frac{1-\cos(x)}{x^2\sin(x)}$$ I keep running in circles using the L'Hospital rule. After the third time applying it I got 0 but this...

The definition of relative primality that I was taught was that: Two numbers are relatively prime if the only common positive factor of the two numbers is...

How do you prove that $$ \Gamma'(1)=-\gamma, $$ where $\gamma$ is the Euler-Mascheroni constant?

The triangular numbers count the number of items in a triangle with $n$ items on a side, like this: This can be calculated exactly by the formula $T_n = \...

folks. I've got this question: Let $D$ be the region $\{(x,y) ~|~ 0 \leq y \leq x, 0 \leq x \leq 1\}$. Evaluate: $$\iint_D (x + y) dxdy$$ by making t...

I am aware that Boole's inequality can be proved by induction. How do we extend these results to an infinite set? (since induction cannot be applied ...

An old alchemist had two sphercial flasks, one with a circunference of $12$ inches and the other one with a circumference of $24$ inches. He desired to tr...

I want to make an origami of a sphere, so I planned to print some net of a pentakis icosahedron, but I have a image of another sphere with more polygons: ...

Let $G=(V,E)$ be a graph with vertices $V$ and edges $E$. Is there standard notation for stating that $\pi$ is a path in $G$? I though about these options...

What is the easiest way to know if large number is divisible by 57? For example, how could I deduce that 57 divides 300000177?