How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions? With induction. I can show that this polynom...

For $0<x<\dfrac{\pi}{4}$ prove that $$\frac{\cos x}{\sin^2x(\cos x-\sin x)}>8$$ I am trying to use the following for x $\in$ (0,$\frac{\pi}{4}$) ...

I have the cartesian coordinates for three points $A$, $B$, $C$. I need to find the angle formed by $A\rightarrow B\rightarrow C$ using the 'right-ha...

When asked to evaluate $\int_{a}^{\infty}f(x)dx$, you split the interval based on the improper points. If there is another improper point other than $\inf...

Basically I tried the matrix \begin{bmatrix} 0 & -1\\ 1 & 0\\ \end{bmatrix} but this eigenvalue of $A^2$ is $1$,and $-1$ which has algebraic multi...

I tried Desmos but it only takes definite integrals (which doesn't make sense to me because a definite integral is a number not a function, but anywa...

Let $G = GL(3,\mathbb{R})$ be the general linear group over the reals , of order $3$ , and let $A\in G$ be : $$ A=\begin{pmatrix} -1 & 0 & 0 \\\ 0...

So I already know how to calculate base area given all 3 edges. I need to use Herom Formula. Now I'm left with finding the height of the prism. What ...

I saw how Russell and Whitehead come to "prove" (may be not, depending on views) that 1+1 = 2. So how does modern logic/set theory prove that 1+1=2? (Is i...

Let $C\subset\mathbb{R}^n$ non-empty. Its polar set $C^\circ$ is defiend as $$C^\circ\equiv \{y\in \mathbb{R}^n\mid \forall x\in C, \,\,\langle y,x\rangle...