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Author: Tinku Tara

prove-that-0-1-e-x-1-e-2x-dx-x-ln-2-1-4-4-2pi-n-1-2n-1-2n-1-n-1-e-

Question Number 140055 by mnjuly1970 last updated on 03/May/21 $$\:\:\:\:\:\: \\ $$$$\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\Omega:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}−{e}^{−{x}} }{\mathrm{1}+{e}^{\mathrm{2}{x}} }\:.\frac{{dx}}{{x}}\:={ln}\left(\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}}\:\right) \\ $$$$\:\Theta:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}}\right)^{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} } \overset{??}…

given-that-x-and-y-are-samples-of-random-variable-drawn-from-a-population-that-is-normally-distributed-find-the-joint-distribution-of-x-and-y-if-x-and-y-are-independent-find-the-marginal-distribut

Question Number 8973 by tekviah munandi last updated on 09/Nov/16 $${given}\:{that}\:{x}\:{and}\:{y}\:{are}\:{samples}\: \\ $$$${of}\:{random}\:{variable}\:{drawn}\:{from}\:{a}\: \\ $$$${population}\:{that}\:{is}\:{normally}\:{distributed} \\ $$$${find}\:{the}\:{joint}\:{distribution}\:{of}\:{x}\:{and}\:{y}.\: \\ $$$${if}\:{x}\:{and}\:{y}\:{are}\:{independent}\:{find}\:{the} \\ $$$${marginal}\:{distributions}. \\ $$ Terms of…

nice-calculus-I-lim-x-pi-4-tan-x-tan-2x-

Question Number 140046 by mnjuly1970 last updated on 03/May/21 $$\:\:\:\:\:\:\:\:\:\:………..\:{nice}\:…….{calculus}\left({I}\right)\:…….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Theta\::={lim}_{\:{x}\rightarrow\:\frac{\pi}{\mathrm{4}}} \:\left(\:{tan}\left({x}\right)\:\right)^{\:{tan}\left(\mathrm{2}{x}\right)} \:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…………………………. \\ $$$$ \\ $$ Commented by mnjuly1970 last updated…