How to evaluate $\cos x=\cos 3x$ on $[0,\pi]$
Question How to evaluate $\cos x=\cos 3x$ on $[0,\pi]$ What I have so far Obviously we can deduce by speculation that $x$ can be $0$ and $1$. But then I d...
Apr 10, 2026 1 VIEWS
Topic: General
5104 Articles 
Why a dotted line in functions?
My question is a little stupid, but I have to ask (I've never seen in anywhere an explanation) I'm studying a very short introduction of categor...
Apr 10, 2026 2 VIEWS
Using Fourier series to determine if a function is odd or even
Determine if the following function is odd or even using Fourier series. $$f(x)=x^5\sin x$$ If a function is even then $b_n=0$ and you have to evaluate $a...
Apr 10, 2026 1 VIEWS
Solving a differential equations and finding the maximum amplitude
This is a practice exercise from my differential equation class: Let $y'' + py' + qy = cos (wt)$ where $p,q,w$ are all positive and let $Ac...
Apr 10, 2026 1 VIEWS
What's the area of one arch of a cycloid?
So, the cycloid is given with parametric equations: $$x=r(t-\sin{t})$$ $$y=r(1-\cos{t})$$ The teacher solved it like this: $$P=\int_a^by(x)dx$$ $x=x(t)$; ...
Apr 10, 2026 1 VIEWS
Upper Bound of Logarithm
For $1\leq x < \infty$, we know $\ln x$ can be bounded as following: $\ln x \leq \frac{x-1}{\sqrt{x}}$. Then what is the upper bound of $\ln x$ for fol...
Apr 10, 2026 1 VIEWS
Finding the range of a function given a specific domain
The question is to "Find the range of each function over the given domain $f(x) = 1 / (2x + 5)$ for $-2 \le x \le 2$. I'm not sure what this is askin...
Apr 10, 2026 1 VIEWS
Dividing a circle into $3$ equal pieces using $2$ parallel lines
I originally found this question in James Stewart's Calculus, specifically in one of the Problems Plus sections. The question asks how $3$ people can...
Apr 10, 2026 1 VIEWS
Mathematical phantoms
The field with one element or characteristic one ($\mathbb{F_1}$ or $\mathbb{F_{un}}$) is a mathematical phantom, which can defined as a beast who clearly...
Apr 10, 2026 2 VIEWS
Verify this identity: $\sin x/(1 - \cos x) = \csc x + \cot x$
Verify this identity $\frac{\sin {x}} {1 - \cos {x}}\ = \csc x + \cot x$ I got the left side to $\frac{1-\cos x} {\csc x}$, but I can't get any farth...
Apr 10, 2026 1 VIEWS
Mutually exclusive events are also independent??
Mutually exclusive events are also independent or not ? can some one explain with an example? Is it compulsory for independent event to be mutually exclus...
Apr 10, 2026 1 VIEWS
Finding the Number of Terms (n) in a Geometric Series When Given $t_1$ to $t_3$ and The Sum?
The sum of the series 6 + 18 +54 + ... to $n$ terms is $2184$. How many terms are in the series? I know this series is geometric since it's constant ...
Apr 10, 2026 1 VIEWS