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Recently on this forum there was a question by a student whether changing the order of integration in the $2D$ or $3D$ case is --in principle-- allowed, and...
Asked on 11/18/2021 by M. Wind
2 answerFind the value of the following integral.$$int_{0}^{4pi} ln|13sin x+3sqrt3cos x|;rm dx$$ My attempt: Using the properties of definite integral, I converted it to this integral.$$4int_{0}^{pi} ln|14sin(x+arctan(frac{3sqrt3}{13}))|;rm...
Asked on 11/18/2021
1 answerIn constrained optimization, an active constraint is generally taken to mean one whose inequality sign can be changed into an equality sign without affecting the optimum. However, I would like...
Asked on 11/18/2021 by Tim Mak
1 answerAccording to the Unscented Transform equations in an Unscented Kalman Filter, sigma points are chosen via: $chi^{[0]}=mu$ $chi^{[i]}=mu+left(sqrt{(n+lambda)Sigma}right)_i;;;i=1,...,n$ $chi^{[i]}=mu-left(sqrt{(n+lambda)Sigma}right)_{i-n};;;i=n+1,...,2n$ where $mu$ is a...
Asked on 11/18/2021 by pcdangio
0 answerI'm taking this Coursera's course on Graph Theory, which is part of a specialization in discrete math for CS, offered by University of California, San Diego: https://www.coursera.org/specializations/discrete-mathematics...
Asked on 11/18/2021 by Daniel Bonilla Jaramillo Haase
1 answerLet $R$ be a Cohen-Macaulay ring and $I$ be an ideal generated by a regular sequence. I want to show that:$bigoplus_{n geq 0}I^{n}/I^{n+1}$ is isomorphic to a...
Asked on 11/18/2021 by user766483
0 answerI'm following Schaum's Outlines for statistics as well as taking a course and I'm getting mixed up with the way hypothesis testing is done for differences of means. First the...
Asked on 11/18/2021
1 answerThe $2$ slices cut into by Lee combine to make one big triangle. I used the Pythagorean theorem to find the...
Asked on 11/18/2021
2 answerQuestion: Find $lim_{nrightarrowinfty}int_0^nfrac{(1-frac{x}{n})^n}{ne^{-x}}dx$. My thoughts: First, I'd like to bring the limit inside the integral, because $lim_{nrightarrowinfty}frac{(1-frac{x}{n})^n}{ne^{-x}}=frac{e^{-x}}{ne^{-x}}rightarrow0$ and $nrightarrowinfty$, and so the value of the integral would...
Asked on 11/18/2021
1 answer$$vec{y}= log{frac{vec{x}}{sqrt[3]{x_1 cdot x_2 cdot x_3}}}$$ Here, $x$ and $y$ are always vectors of length 8 and all elements of $x$ are greater than $0$....
Asked on 11/16/2021
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