Prove $$ \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=\frac{1}{r}\frac{\partial}{\partial r}\left(r\frac{\partial u}{\partial r}\ri...

I don't understand the answer, why does $p'(z)$ equal to that equation? And why does that equation dividing by p(z) yield the final answer?

How can I prove the following identity: $$(\vec{a}\times\vec{b})\cdot(\vec{c}\times\vec{d}) = (\vec{c}\cdot\vec{a})(\vec{b}\cdot\vec{d})-(\vec{b}\cdot\vec...

I have something like this $$ h(x) = f(x) g(x) $$ where $f$ and $g$ are some nice functions such that $f$ is $[0,1]$-bounded, concave function and $g$ is ...

If a function is not continuous, does it mean it has no limit? If it's false can you give me an example? It's not homework I really want to unde...

The following sets do not match. D[(a*x+b*y[x]-x*(a*x+b*y[x])-y*(c*x + d*y[x]))*x, {x,1}] (correct answer) (a x + b y - x (a x + b y) - y (c x + d y) ) 　...

Here is the question: The dome over a town hall has a parabolic shape. The dome measures 48 m across and rises 12 m at its centre. a) Determine the quadra...

How to solve this inequality? $$\arccos(x) \gt \arccos(x^2)$$ I've brushed up on arccos and it's basically the inverse function of the cosine an...

I'm learning about sets and I've come across this question. {x} ∈ {{x}} I have to answer whether this statement is true or not. I put down true ...

I've calculated the area inside the circle $r=3a\cos(\theta)$ and outside the cardioid $r=a(1+\cos(\theta))$ and I got two answers: $a^2\pi + a^2\fra...