This question arose after my calculus test in which the told us: Show that $$f(x,y)=\begin{cases}\frac{2x^3}{x^2 +y^2}&\text{ if }(x,y)\neq(0,0)\\0&am...

I am reviewing my analysis notes, and having trouble understanding certain parts of the proof to Lusin's theorem. $\textbf{Lusin's Theorem}$: Le...

True or false? $S_{3}$ has a subgroup of order $5$. $S_3$ is the group of all permutations of the numbers $1,2,$ and $3$. An example of a permutation is, ...

Im trying to figure out what degree exactly you get when you first translate and then rotate or the other way around. I'm trying it without coordinat...

How many different groups are there in order 8? And how do I know which groups they are? I mean, is there anyone can teach me to calculate them? I want a ...

I have this equation: $$\lim_{n\to \infty}\left(1+{x\over n} \right)^n=e^x$$ I need to Taylor expand both sides to prove that they are equal. Now I know h...

I've encountered an unusual shape that I have no idea the name of. We have a sticker on the shape that tells us the equation $z^2 = \frac{x^2}{a^2-y^...

$x^2+6x+8=0$ you can factorise this to $(x+4) \cdot (x+2)=0$ and it's quite obvious that there are two solutions and why they work. you can also solv...

There is the choice between four trigonometric identities $$\sin(4\phi)=8\cos^{3}(\phi)\sin(\phi)-4\cos(\phi)\sin(\phi)$$ $$\cos(4\phi)=8\cos^{4}(\phi) -8...

If we have a function $f(x)$ that is equal to $\frac{g(x)}{h(x)}$, then the limit laws tell us that $\lim \limits_{x \to a} f(x) = \frac{\lim \limits_{x \...