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

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

Riemann Lebesgue Lemma application February 11    1

Riemann Lebesgue Lemma. shows that if $f \in L^1 ( \bf R)$ then the Fourier transform of $f$ goes to $0$.Does this also implies that $f(x) \to 0$ as $\vert x \vert \to \infty$ That is implied by $f \in L^1(\mathbb{R})$AnalysisStudent04141 12

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?

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

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