Why is this not correct: $$ \begin{align} \lim_{n\to \infty}\sqrt[n]{n!} &= \lim_{n\to \infty}\sqrt[n]{n(n-1)(n-2)(n-3)\cdots(1)} \\ &=\lim_{n\to ...

Little confused on the rules here, obviously if I treat it as a vector and its transpose I can compute this if I knew each vector entry but I am keen to k...

In one of my proofs, I wrote "Assume, {stating inductive hypothesis}" and in inductive step "We know that ... holds for k-1" instead of writing "Inductive...

In my text book it is written that if $$\lim_{x\to0}\;\frac{\cos(4x) + a\cos(2x) + b}{x^4}$$ is finite then $\frac{\cos(4x) + a\cos(2x) + b}{x^4}$ should ...

In order to arouse interest of my high school students to plot graphs I want to plot interesting funny graphs such as the one of the batman equation. I�...

I understand that the standard form of a hyperbola is $$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} = 1$$ and I also know that via algebra we can make this ge...

Let G be a graph of maximum degree ∆. Show that it is possible to assign integers to all edges of G in such a way that any path P = $v_1...v_l$ in which t...

Let A be the hyperbola with the equation $\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, where $a$ is the $x$-intercept and $b$ is the $y$-intercep...

Is there a formal proof of this fact without using L'Hôpital's rule? I was thinking about using a proof of this fact: $$ \left.\frac{d(e^{x})}{d...

Let $G$ be a finite group, and $X$ a free topological $G$-space which admits a CW-structure. Is there a CW-structure on $X$ that compatible with its $G$-a...