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Euler's Method on differential equation
For a differential equation, it is known that Euler’s Method leads to an underestimate when the curve is concave up, just as it will lead to an overestima...
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Is a ring R a progenerator for the category R-mod?
I have to demonstrate that $R$ viewed as left $R$-module is a progenerator (i.e. a projective and finitely generated generator) of $R$-mod, the category o...
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What is the most elegant and simple proof for the law of cosines?
Given 2 sides, and an angle between those two sides, what is the simplest proof you can come up with to find the measure of the 3rd side?
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Integrate $\int \sin^4x \cos^2x dx$
Integrate $$\int \sin^4x \cos^2x dx$$ Now, there's few solutions to this problem already on the internet. For example on yahoo: https://answers.yahoo...
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If $f_n \to f$ and $g_n \to g$ in measure and $\mu$ is finite, then $f_n g_n \to fg$ in measure
This is Problem 3.1.5 in Cohn's Measure Theory, 2nd edition. Let $\mu$ be a measure on $(X, \mathcal A)$, and let $f, f_1,f_2, \ldots$ and $g,g_1,g_2...
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Find sum of all integer solution of $\frac{2}{a} + \frac{3}{b} + \frac{4}{c} + \frac{5}{d} = \frac{1}{14}$
Given $\frac{2}{a} + \frac{3}{b} + \frac{4}{c} + \frac{5}{d} = \frac{1}{14}$ , which $a,b,c ,d$ are an positive integer , all solution of $a,b,c,d$ are me...
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If the spinner is spun 2 times what is the probability that it lands on "A" both times
If the spinner is spun 2 times what is the probability that it lands on "A" both times. My answer is 3/16 and here is how I got it: I divided the whole ci...
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What algorithm is used by computers to calculate logarithms?
I would like to know how logarithms are calculated by computers. The GNU C library, for example, uses a call to the fyl2x() assembler instruction, which m...
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Poisson-Jensen Formula; zero or poles on $|z| = R$
For the proof of the Poisson-Jensen formula, I want to show that the following equality holds: $$\log(|z-a|) = \int_{0}^{2\pi} \log(|Re^{i\theta} - a|) P(...
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Name of Famous Triangle Area Formula? $A=\frac{1}{2}ab\sin(C)$
I'm sorry for this short question, but I really could not find the answer to this anywhere. Is there a name for the formula $A=\frac{1}{2}ab\sin(C)$?
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