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Question-173721

Question Number 173721 by KONE last updated on 16/Jul/22 Answered by mnjuly1970 last updated on 17/Jul/22 $$\:\:{e}^{\:\mathrm{ln}\left(\mathrm{lim}_{{n}\rightarrow\infty} \left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\sqrt[{{n}}]{{e}}\:\left(\frac{\mathrm{2}}{\pi}\:\right)^{\frac{\mathrm{1}}{{k}^{\:\mathrm{2}} }} \right)\:\right)} \\ $$$$\:\:\:\:\:\:=\:{e}^{\:\mathrm{lim}_{\:{n}\rightarrow\infty} \left(\underset{{k}=\mathrm{1}}…

strange-behavior-in-editor-when-you-have-written-for-example-12-13-and-you-want-to-delete-13-and-change-to-24-it-is-not-possible-this-occurs-also-in-other-cases-

Question Number 108181 by mr W last updated on 15/Aug/20 $${strange}\:{behavior}\:{in}\:{editor}: \\ $$$${when}\:{you}\:{have}\:{written}\:{for}\:{example} \\ $$$$\frac{\mathrm{12}}{\mathrm{13}}\:{and}\:{you}\:{want}\:{to}\:{delete}\:\mathrm{13}\:{and} \\ $$$${change}\:{to}\:\mathrm{24},\:{it}\:{is}\:{not}\:{possible}. \\ $$$${this}\:{occurs}\:{also}\:{in}\:{other}\:{cases}. \\ $$ Commented by mr W…

If-x-y-R-x-2-xy-4-0-ax-2-b-y-2-x-4a-0-Find-the-minimum-of-a-2-1-2-b-2-

Question Number 108171 by ZiYangLee last updated on 15/Aug/20 $$\mathrm{If}\:{x},{y}\in\mathbb{R} \\ $$$${x}^{\mathrm{2}} −{xy}+\mathrm{4}=\mathrm{0} \\ $$$${ax}^{\mathrm{2}} +\left({b}+{y}^{\mathrm{2}} \right){x}+\mathrm{4}{a}=\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:{a}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}{b}^{\mathrm{2}} \\ $$ Answered by mr…

solve-for-x-1-3-log-x-3-log5-log-x-2-2-0-

Question Number 42627 by mondodotto@gmail.com last updated on 29/Aug/18 $$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{\mathrm{log}}\left(\boldsymbol{{x}}−\mathrm{3}\right)+\boldsymbol{\mathrm{log}}\mathrm{5}−\boldsymbol{\mathrm{log}}\left(\boldsymbol{{x}}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{0} \\ $$ Answered by $@ty@m last updated on 30/Aug/18 $$\mathrm{log}\:\left({x}−\mathrm{3}\right)+\mathrm{3log}\:\mathrm{5}−\mathrm{3log}\:\left({x}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{log}\:\mathrm{1} \\…

Question-108162

Question Number 108162 by mathdave last updated on 15/Aug/20 Answered by JDamian last updated on 15/Aug/20 $${k}={m}−\mathrm{4}\:\:\Rightarrow\:\:{m}={k}+\mathrm{4} \\ $$$$ \\ $$$$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{2}^{{k}+\mathrm{4}} }{\left({k}+\mathrm{4}\right)!} \\…