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How to approximate $\pi$ using the Maclaurin series for $\sin(x)$
We have that $$\sin(x)=x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots$$ Now plugging in $x=\pi$, $$0=\pi - \frac{\pi^3}{3!} + \frac{\pi^5}{...
Apr 11, 2026
Archive: News
![Does probability have a memory? [closed]](https://news.conceivablytech.com/uploads/does-probability-have-a-memory-closed_720.jpg)
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Does probability have a memory? [closed]
If I flip a perfect coin, the chance of heads is obviously 0.5 with each toss. Equally obviously, if I toss 3 times in a row, the probability of getting 3...
Apr 11, 2026
news
3x3 System with No Solution
I have the system of equations as follows: $x + y + z =0$ $2x + 3y + 2z = -3$ $-x - 2y -z = 1$ First I added the first and third equation and the result w...
Apr 11, 2026
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Sketch the graph of a function that satisfies all of the stated conditions
The conditions are: $\lim_{x\rightarrow\infty}f(x)=1$ $\lim_{x\rightarrow-\infty}f(x)=2$ $\lim_{x\rightarrow-2^-}f(x)=\infty$ $\lim_{x\rightarrow-2^+}f(x)...
Apr 11, 2026
news
Subtraction of inequalities
Suppose I have two inequalities: $$k_1 \leq a$$ $$k_2 \leq b$$ where $k_1,k_2,a,b$ are all positive numbers I know that that summation of them can be writ...
Apr 11, 2026
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Fourier series expansion of Dirac delta function
My question is from Arfken & Weber (Ed. 7) 19.2.2: In the first part, the question asks for Fourier series expansion of $\delta(x)$. I have found $$\d...
Apr 11, 2026
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Weird "hidden answer" in $2\tan(2x)=3\text{cot}(x)$
The question is Find the solutions to the equation $$2\tan(2x)=3\cot(x) , \space 0<x<180$$ I started by applying the tan double angle formula and re...
Apr 11, 2026
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Can we extend the proof of density of $\sin(n)$ to $\sin(n^2)$?
We know that $(x_n)_{n\in\mathbb{N}} $ defined as $x_n=\sin(n) $ is dense in the interval $[-1,1]$ , can we extend this to prove also $\sin(n^2) $ is dens...
Apr 11, 2026
news
Proof for infinity matrix norm
I need to prove the infity norm of a matrix, which is here: $$||A||_\infty = \max_{x \neq 0}\left\{\frac{\max_{1\le i\le n}(|(Ax)_i|)}{\max_{1 \le i \le n...
Apr 11, 2026
news
If yesterday were tomorrow, then today would be Friday.
(S) If yesterday were tomorrow, then today would be Friday. Question: What day is today? This seems to be an old puzzle, and depending on the interpretati...
Apr 11, 2026
