Mathematics
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Angelo
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View all questions and answers
All Questions Answers
Score Newest
question
18
An interesting limit: $\lim_\limits{n\to\infty}\frac{\sin 1\sin\sqrt{1}+\sin 2\sin\sqrt{2}+\sin 3\sin\sqrt{3}+\cdots+\sin n\sin\sqrt{n}}{n}$
Aug 12, 2020
answer
17
Conjecture: If matrix $M$ has entries (left to right, then top to botom) $\sin 1,\sin 2,\sin 3,\dots,\sin (n^2)$, where $n\ge 3$, then $\det M = 0$.
Sep 9
answer
13
For orthogonal matrices $A$ and $B$, prove $\det(A^{t}B - B^{t}A)=\det(A+B)\det(A-B)$
Jan 21
answer
12
Show that $\sqrt{10}+\sqrt{26}+\sqrt{17}+\sqrt{37} \gt \sqrt{341}$
Aug 16
answer
10
Product of limit, sin, infinity, error?
Feb 24
answer
10
Evaluate the integral $\int\limits_0^\infty {{{\left( {\frac{e}{x}} \right)}^x}\Gamma \left( x \right)\sin \left( {2\pi x} \right)dx}$
May 1
answer
8
verifying $\lim\limits_{x \to \infty} (1+\frac{1}{\sqrt{x}})^x$
Jul 12, 2020
answer
8
Prove : $\int_{{π}/{4}}^{{π}/{2}} e^{\cos x + \cos^2{x}}\mathrm dx>\sqrt2$
May 26
answer
7
$\langle x,y \rangle (\lVert x \rVert + \lVert y \rVert) \leq \lVert x \rVert \lVert y \rVert \lVert x+y \rVert$
Sep 20, 2020
question
7
Calculating $\;\int_{-\infty}^{\infty}\frac{1}{(e^x-1-x)^2+4\pi^2}~dx$
Apr 30

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