Menu Close

Author: Tinku Tara

Question-213656

Question Number 213656 by efronzo1 last updated on 12/Nov/24 Answered by golsendro last updated on 13/Nov/24 $$\:\:\left(\mathrm{i}\right)\:\mathrm{g}\left(\mathrm{4}−\mathrm{x}\right)=\:−\mathrm{g}\left(\mathrm{x}\right)\: \\ $$$$\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\mathrm{g}\left(\mathrm{4}−\mathrm{x}\right)\mathrm{dx}\: \\ $$$$\:\:\:\:\:\:\:\:\underset{\mathrm{0}}…

Question-213641

Question Number 213641 by Abdullahrussell last updated on 12/Nov/24 Answered by Ghisom last updated on 12/Nov/24 $$\alpha_{{k}} \in\mathbb{Z} \\ $$$${p}\left({x}\right)=\underset{{k}=\mathrm{3}} {\overset{{n}} {\sum}}\alpha_{{k}} {x}^{{k}} \\ $$$${x}\in\mathbb{Z}\:\Rightarrow\:{p}\left({x}\right)\in\mathbb{Z}…

Question-213642

Question Number 213642 by universe last updated on 12/Nov/24 Answered by Berbere last updated on 12/Nov/24 $${a}_{{n}} =\underset{{N}\rightarrow\infty} {\mathrm{lim}}\underset{{k}={n}} {\overset{{N}} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}} };\forall{k}\geqslant{n}>\mathrm{1}\:\:{k}\left({k}−\mathrm{1}\right)\:\leqslant{k}^{\mathrm{2}} \leqslant{k}\left({k}+\mathrm{1}\right)\Rightarrow \\ $$$$\underset{{N}\rightarrow\infty}…

Question-213639

Question Number 213639 by efronzo1 last updated on 12/Nov/24 Answered by golsendro last updated on 12/Nov/24 $$\:\:\:\mathrm{8}^{\mathrm{x}} =\mathrm{25}^{\mathrm{y}} =\:\mathrm{t}\:\Rightarrow\begin{cases}{\mathrm{x}=\:\mathrm{log}\:_{\mathrm{8}} \mathrm{t}}\\{\mathrm{y}=\:\mathrm{log}\:_{\mathrm{25}} \mathrm{t}}\end{cases} \\ $$$$\:\:\Rightarrow\mathrm{8}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{25}\left(\frac{\mathrm{1}}{\mathrm{y}}\right)=\:\mathrm{1} \\ $$$$\:\:\:\mathrm{8}.\:\mathrm{log}\:_{\mathrm{t}}…

a-m-h-m-1-h-2-pi-2-6-h-1-m-1-h-2-a-m-1-m-1-n-z-d-n-1-dz-n-1-ln-z-C-Z-0-aka-polygamma-function-1-lim-m-m-1-m-1-1-and-

Question Number 213648 by issac last updated on 12/Nov/24 $${a}_{{m}} =\underset{{h}={m}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{h}}\right)^{\mathrm{2}} =\frac{\pi^{\mathrm{2}} }{\mathrm{6}}−\underset{{h}=\mathrm{1}} {\overset{{m}} {\sum}}\:\left(\frac{\mathrm{1}}{{h}}\right)^{\mathrm{2}} \\ $$$${a}_{{m}} \approx\boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left({m}+\mathrm{1}\right) \\ $$$$\boldsymbol{\psi}^{\left({n}\right)} \left({z}\right)=\frac{\mathrm{d}^{{n}+\mathrm{1}} \:\:}{\mathrm{d}{z}^{{n}+\mathrm{1}}…