In my study of groups, rings, modules etc, I've seen the three isomorphism theorems stated and proved many times. I use the first one ( $G/\ker \phi ...

The graph of a quadratic function has $x$-intercepts $-1$ and $3$ and a range consisting of all numbers less than or equal to $4$. Determine an expression...

In $\mathsf{ZF}$ we have the Power Set Axiom: if $x$ is a set, then $\mathcal P(x)$ is a set (see here for a nice listing of the axioms of $\mathsf{ZF}$)....

How do I prove that the limit of the following function is $1$? $\displaystyle\lim_{x\to \pi/2} (\tan x)^{\tan2x}$ I shouldn't use l'Hôpital...

Q&A for people studying math at any level and professionals in related fields

Let $A \in \mathbb{R}^n$ be a positive definite matrix. Then, it is well known that \begin{align} \text{Tr}(A^{-1}) \ge n^2 \text{Tr}(A)^{-1} \end{align} ...

I want to graph a simple equation $f(x)$ which begins at $(0,1)$, then for every increasing $x$ integer increment, $f(x) = f(x-1) - (c * f(x-1))$. So in o...

In my calculator (TI-84), there are only $sin, cos,$ and $tan$ commands (and inverse sin, inverse cos, inverse tan). I had a question that was as follows:...

I have a homework problem for my intro computation class where I have to write a regular expression for an NFA. In order to help understand if my language...

I apologize in advance if this question is trivial to most of you but I'd like to verify if my understanding is correct. I want to verify the followi...