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...

I understand that the shadow of an object is one dimension less than the original object. What what the shadow of a tesseract look like? Are there any rea...

$$ _{1}F_{2}\left(n-\frac{1}{2};n+1,2n+1;-x^{2}\right)=\frac{2^{2n+1}\Gamma^{2}(n+1)}{x^{2n}(2n+1)}\left(\left(xJ^{'}_{n}(x)+\frac{J_{n}(x)}{2}\right...

What is the graph of $x^{\log y}=y^{\log x}$? This question appears on GRE exam.

I'm struggling with this problem: For any natural number $n$, prove that $n^3 + 3n^2 + 2n$ is a multiple of $3$. That $n^3 + 3n^2 + 2n$ is a multiple...

Find the matrix representation of the linear transformation $\alpha:\mathbb{R}^3 \rightarrow \mathbb{R}^2$ defined by $$\alpha : \begin{pmatrix} a\\b\\c \...

I generaly find the definition of polygon as a "polygonal chain", but I barely find another definition that defines a convex polygon as the intersection o...

I am solving problem (Linear Algebra by Hoffman, Excercise 5.4.8) : Let $V$ be the vector space of $n\times n$ matrices over the field $F$. Let $B$ be a f...

Is it correct? $\neg$(a and b)=(not a) or (not b) What ruleset can i look up for negations? Especially for "all", "if, then" statements.