## Trianglessin, cos etc. February 11

I know this is a quite simple question for most of you out there.However it has been a little troubling for me, and would like to get a little help if possible.I have a triangle ABC where I know thatC = 29° a = 5,2 and T = 8,4What I have to find out

## Why does this function converge point-wise to $0$ February 11    2

Let $$f_n(x) = \begin{cases} \sin nx & 0 \leq x \leq \frac\pi n\\ 0 & x \geq \frac\pi n \end{cases}$$Then my book says that $f_n \to f \equiv 0$ on the interval $[0, +\infty)$.I don't understand why $0$ is included. I think that the interval of co

## Series converges point-wise February 11

$f_{n}=\sum_{i-=1}^{\infty }\frac{x^{4}}{(1+x^{4})^{n}}$Show that it converges point-wise on R, but not uniformly on R.My attempt:I think, we should use Weierstrass's M test for uniform convergence would you please help me to solve this problem

## Is category theory ambiguous or it just is the case for beginners February 11

First of all, I have to say that I'm not going to offend anyone/anything here; I just need some clarification/studying tips about category theory.I was reading the principle of duality (from Awodey's text). He seems to be too wordy and honestly speak

## Kernel of a map $\phi: \mathbb{C}^3 \to \mathbb{C}^2$ February 11    1

I cannot understand which is the kernel of the following map $\phi: \mathbb{C}^3 \to \mathbb{C}^2$ with $$(t_1,t_2,t_3) \mapsto \left(\frac{t_2}{t_1}, \frac{t_3}{t_1}\right)$$ In other words I do not see which elements of $\mathbb{C}^3$ map to zer

## Closed Form and Pullback compatibility February 11

given:$U,V \subset \mathbb{R}^N, f\in C^1(V,U)$ a diffeomorphism Let $\omega$ be a k-Form on U and $f^*\omega$ a closed Form.Then with $0 = df^*(\omega) = d \omega(df)$ we have ,that $\omega$ is a closed Form. Is this correct?

## What would be simple way of calculating the area of a 3D PieChart's slices February 11

I have created a 3D Pie Chart able to be rotated. ->http://plnkr.co/edit/QIYu8sJUWPmxcby1ky9l?p=previewI did it to demonstrate how the visual perception of data in a Pie Chart can be distorted depending on the position, so that with a 3D pie chart, t

## The Shapley value and the core February 11

I had one task on exam, which confused me, can you give me some ideas ? The task was: We know that $(1,1,1,1,1)$ belong to the core. What can we tell about the Shapley value? I think the only thing we can tell is that if $(x_1,x_2,x_3,x_4,x_5)$ is a

## $(M, \mathcal{M}_C, \mu_{1/2}$ is a measure space wher $C$ is the cantor set. February 11

I am trying to show $(M, \mathcal{M}_C, \mu_{1/2}$) is a measure space where $\mu_{1/2}$ is defined as:$$\mu_{1/2}(I_{\underline{\omega}}) = \frac{1}{2^n}$$given $I_{\underline{\omega}} = I_{\omega_0 \omega_1 \omega_2 ..... \omega_n}$ is an inter

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