Question involving the Divergence Theorem and Surface Integrals

Thread starter lys04
Start date Jun 14, 2024
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Calculus Gradient Vector

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The discussion centers on the proper use of LaTeX for posting mathematical content, specifically regarding the Divergence Theorem and surface integrals. Users emphasize the importance of avoiding image uploads in favor of LaTeX to enhance readability and facilitate quoting. The original poster acknowledges the feedback and agrees to use LaTeX in future posts. The conversation highlights the community's preference for clear, text-based mathematical expressions over images. Overall, the forum encourages best practices for sharing complex mathematical ideas.

Jun 14, 2024

lys04

Homework Statement: Divergence theorem problem

Relevant Equations: Divergence theorem, surface integrals

Is this correct? Ignore my bad drawings

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Jun 14, 2024

Orodruin

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It looks fine, but in the future please do not simply post images. The forum has a perfectly functioning LaTeX implementation, use it! If you just post a screenshot of your compiled math there is no possibility for us to quote particular sections of your post and it is less readable.

Jun 14, 2024

lys04

Will do! Thanks

Thread 'Does this series converge uniformly?'

First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...

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