# All Questions

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### why measure theory

I studied elementary probability theory. For that, density functions were enough. What is a practical necessity to develop measure theory? What is a problem that cannot be solved using elementary ...
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### Importance of Neatness / Organization / Speed in Math?

Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes. How important is neatness in math? Does having messy writing put ...
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### When is integration possible? [duplicate]

I'm not sure how to phrase this question. I'm sure I could write it in terms of operators between Frechet spaces, or something like that. Let me apologies to any analysts in advance for my lack of ...
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### System of Differential Equations Question Assistance

The following question has just left me confused with no real decent avenue of attack so any assistance on this would be appreciated. For the system of equations $t {\frac{d \vec x}{dt}} = A\vec x$ ...
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### Irreducibility of $x^n-x-1$ over $\mathbb Q$

I want to prove that $p(x):=x^n-x-1 \in \mathbb Q[x]$ for $n\ge 2$ is irreducible. My attempt. GCD of coefficients is $1$, $\mathbb Q$ is the field of fractions of $\mathbb Z$, and $\mathbb Z$ ...
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### How do I prove Poisson appraches Normal distribution

I want to prove why the mean and variance of a $\operatorname{Poisson}(\lambda)$, is different when the time index approaches infinite (it's approximated by the mean and variance of a Normal). For ...
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### Confusing symbol in papers on hybrid logic

In literature about hybrid logic I'm reading for my thesis I've come across the following symbol: ::= Now, I've never seen this notation before. I can also not ...
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### Decreasing from the horizontal asymptote

The function $f(x) = x^2/(x^2 - x -2)$ has the following graph. It has a horizontal asymptote $y=1$. For $x$ less than $-4$, the function is decreasing and its graph is under the asymptote. How is ...
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### Taylor Polynomial for $x^{1/3}$

a. Compute the Taylor polynomial $T_3(x)$ for the function $(x)^{1/3}$ around the point $x=1$. b. Compute an error bound for the above approximation at $x = 1.3$. I'm having trouble figuring ...
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### Mathematica vs Wolfram Alpha integration results

When I insert the following integration command in wolframalpha: ...
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### Which of the following are subspaces of $M$?

Let $M$ be a vector space of all $3\times 3$ real matrices and let $$A=\begin{pmatrix}2&3&1\\0&2&0\\0&0&3\end{pmatrix}.$$ Which of the followings are subspaces of $M?$ ...
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### Symmetrically splitting an octagon into quadrilaterals

I'm wondering whether it is possible to split an octagon into a finite number of quadrilaterals, such that the result is symmetric from all 8 directions (sides or points). There is one condition — any ...
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### Trap Rule for sin(x)

Use the trapezoidal rule with $N=6$ to approximate the arc length of the curve $f(x) = \sin(x)$ from $x=0$ to $x=\pi$. So I found that $\Delta x = \frac{\pi}{6}$ which means that my interval ...
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### How to prove the existence of infinitely many $n$ in $\mathbb{N}$,such that $(n^2+k)|n!$

Show there exist infinitely many $n$ $\in \mathbb{N}$,such that $(n^2+k)|n!$ and $k\in N$ I have a similar problem: Show that there are infinitely many $n \in \mathbb{N}$,such that ...
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### Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$

Let $f(x) = x^2 \sin{\frac{1}{x}}$ for $x\neq 0$ and $f(0) =0$. (a) Use the basic properties of the derivative, and the Chain Rule to show that $f$ is differentiable at each $a\neq 0$ and ...
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### On finding adjoint of transformation.

Let $V$ be an inner product space and $v,w\in V$ be fixed vectors. Define $T(u)=(u,v)w$. How to find the adjoint mapping $T^*$?
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### What is the proper way to determine error in my measurements?

How do I know what the error is in measurements I took using an oscilloscope? In the image below you will see on channel #1 of the oscilloscope (yellow) there is a pattern. I manually measured the ...
### find the dimension of $W.$
Let $W=\{p(B):p \text{ is a polynomial with real coefficients}\},$ where $B=\begin{pmatrix}0&1&0\\0&0&1\\1&0&0\end{pmatrix}.$ Then find the dimension of $W.$ I have shown ...