Prove multi-dimensional Mean Value Theorem
I've been asked to prove multi-dimensional Mean Value Theorem. I'd be grateful if someone could give me feedback if it is okay. Proof of Mean Va...
19 Apr 2026 1 READS
Archive: News
what is the symbol generally used for whole numbers?
For subjecting to whole numbers, what symbol should I use? it must be valid for using anywhere from school to college. The symbol should be known and well...
19 Apr 2026 1 READS
The Cardinality of the Surreal Numbers and Games
I've been learning about John H Conway's surreal numbers, which are a rich superset of the reals. It's clear that the real numbers are dens...
19 Apr 2026 1 READS
![Integration of $\sin(2x)$ via two different methods [duplicate]](https://edu.smbbmcl.edu.pk/uploads/integration-of-sin-2x-via-two-different-methods-duplicate_720.jpg)
Integration of $\sin(2x)$ via two different methods [duplicate]
When I integrate $\sin(2x)$ first using the trig substitution of $\sin(2x) = 2 \sin x\cos x$ and then using u-substitution I get $\sin^2(x) +C$. Integrati...
19 Apr 2026 1 READS
Lagrange multiplier question with unit circle constraint
I'm having trouble with the following question: Show $|ax + by| \leq (a^{2} + b^{2})^{1/2}$ if $x^{2} + y^{2} = 1$ by finding the maximum and minimum...
19 Apr 2026 1 READS
Solve for the angle x?
The problem seems really impossible to me, despite solving many problems on triangles. So I hope that you can solve it. src:https://www.instagram.com/p/Bt...
19 Apr 2026 1 READS
Finding the angle a vector makes with the 'horizontal'
Suppose a cable car moves with direction vector $\vec{d}$ = $$\begin{pmatrix} 2\\ -2\\ 1\\ \end{pmatrix} $$ The question asks, "at what angle to the ...
19 Apr 2026 1 READS
Why can't you square both sides of an equation?
Why can't you square both sides of an equation? I've been asked this many times and can never quite give a good, clear, concise answer (for begi...
19 Apr 2026 1 READS
Find $x,y \in \mathbb C $ such that $x^5+y^5=275, x+y=5$.
My attempt: Let $x, y$ be roots of $$t^2-5t+p=0$$ I got $$p=\frac{5 \pm \sqrt{-431}}{2}$$ using Vieta's relations. Now I just calculated x and y usin...
19 Apr 2026 1 READS
How to evaluate $(0.9)^4$ without calculator
How can I evaluate $0.9^4$ without a calculator? I think I have to use the binomial theorem but I don't know exactly how it works. It should be in th...
19 Apr 2026 1 READS
