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Category: Algebra

e-e-e-1-3-e-1-4-e-1-5-e-1-6-e-1-7-e-1-8-

Question Number 88360 by jagoll last updated on 10/Apr/20 $$\frac{\mathrm{e}}{\:\sqrt{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{3}\:\:}]{\mathrm{e}}}{\:\sqrt[{\mathrm{4}\:\:}]{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{5}\:\:}]{\mathrm{e}}}{\:\sqrt[{\mathrm{6}\:\:}]{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{7}\:\:}]{\mathrm{e}}}{\:\sqrt[{\mathrm{8}\:\:}]{\mathrm{e}}}×…=? \\ $$ Commented by john santu last updated on 10/Apr/20 $$=\:{e}^{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{6}}+…} \\ $$$$\left[\:\mathrm{ln}\:\left(\mathrm{1}+\mathrm{x}\right)\:=\:\mathrm{x}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{x}^{\mathrm{4}}…

Determine-whether-there-exists-2016-distinct-prime-numbers-p-1-p-2-p-2016-and-positive-integer-n-such-that-i-1-2016-1-p-i-2-1-1-n-2-

Question Number 153899 by mathdanisur last updated on 11/Sep/21 $$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{there}\:\mathrm{exists}\:\:\mathrm{2016} \\ $$$$\mathrm{distinct}\:\mathrm{prime}\:\mathrm{numbers}\:\:\mathrm{p}_{\mathrm{1}} ,\mathrm{p}_{\mathrm{2}} ,…,\mathrm{p}_{\mathrm{2016}} \\ $$$$\mathrm{and}\:\mathrm{positive}\:\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{such}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{i}}=\mathrm{1}} {\overset{\mathrm{2016}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{p}_{\boldsymbol{\mathrm{i}}} ^{\mathrm{2}} \:+\:\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} } \\ $$…

Find-all-functions-f-Q-Q-satisfying-these-followong-conditions-for-all-x-Q-1-f-x-1-f-x-1-2-f-x-3-f-3-x-

Question Number 153898 by mathdanisur last updated on 11/Sep/21 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{functions}\:\:\mathrm{f}:\mathrm{Q}\rightarrow\mathrm{Q}\:\:\mathrm{satisfying} \\ $$$$\mathrm{these}\:\mathrm{followong}\:\mathrm{conditions}\:\mathrm{for}\:\mathrm{all}\:\boldsymbol{\mathrm{x}}\in\mathrm{Q} \\ $$$$\mathrm{1}.\:\mathrm{f}\left(\mathrm{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{1} \\ $$$$\mathrm{2}.\:\mathrm{f}\left(\mathrm{x}^{\mathrm{3}} \right)\:=\:\mathrm{f}^{\:\mathrm{3}} \left(\mathrm{x}\right) \\ $$ Answered by talminator2856791 last updated…

find-the-minimum-and-maximum-value-of-5-f-3-where-f-8cos-15-sin-

Question Number 153870 by physicstutes last updated on 11/Sep/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{of}\:\frac{\mathrm{5}}{{f}\left(\theta\right)+\mathrm{3}}\:\mathrm{where}\:{f}\left(\theta\right)=\mathrm{8cos}\:\theta−\mathrm{15}\:\mathrm{sin}\:\theta \\ $$ Commented by mr W last updated on 12/Sep/21 $${there}\:{are}\:{no}\:{minimum}\:{and}\:{no} \\ $$$${maximum}.\:{there}\:{are}\:{only}\:{local}\:…