# All Questions

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### Showing that $\int_{-n}^{n}{x+\tan{x}\over A +B(x+\tan{x})^{2n}}dx=0$

Where n is an integer, $n\ge1$ and $(A,B)$ just constants $$I=\int_{-n}^{n}{x+\tan{x}\over A +B(x+\tan{x})^{2n}}dx=0$$ It is obvious that $$\int_{-n}^{n}x+\tan{x}dx=0$$ Let make a ...
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### equation of a circle that has a radius of $\sqrt{10}$

I am supposed to find the equation of a circle that has a center $(\sqrt{5},2\sqrt{2})$ and a radius $\sqrt{10}$. I have no idea of solving an equation which the given center ($\sqrt{5},2\sqrt{2})$. ...
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### Metric hyperbolic polar

The metric tensor hyperbolic is given by $$g=4\frac{\mathrm d x^2+\mathrm d y^2}{(1-x^2-y^2)^2}.$$ I have to right it in polar. I know that the euclidien metric $\mathrm d x^2+\mathrm d y^2$ is given ...
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For a function $f\in C^2$, $f:\mathbb{R}^n\to\mathbb{R}$ and a point $x\in\mathbb{R}^n$ with $\nabla^2f(x)$ positive definit one can calculate the new point $x^+=x+s$ as follows: Change the ...
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### An integral inequality $\int_0^{π/2} t\left(\frac{\sin(nt)}{\sin t}\right)^4 dx \lt \frac{π^2n^2}{4}$ [duplicate]

QUESTION: $$\int_0^{π/2} t\left(\frac{\sin(nt)}{\sin t}\right)^4 dx \lt \frac{π^2n^2}{4}$$ I guess it should be divided, but I couldn't find out the way to prove it.
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### On the equation $|x|^2+|x|-6=0$

Which of the following are true for $$|x|^2+|x|-6=0$$ 1. It has $4$ roots 2. The sum of the roots is $-1$ 3. The product of the roots is $-4$ 4. The product of the roots is $-6$ Only one of the ...
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### How does the following graph have an Euler tour and not every node has degree that is even?

The theorem states: A connected graph has an Euler tour if and only if every vertex has even degree. But this graph has node 'A' with degree = 3. Graph image. ...
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### Probability: Application Of “Expected Value”

So, I was learning expected value today and I'm trying to understand the significance of calculating this term "Expected value". In this simple example, What is the expected value when we roll a ...
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