Question Number 102234 by Harasanemanabrandah last updated on 07/Jul/20 Answered by OlafThorendsen last updated on 07/Jul/20 $${f}\left({x}\right)\:=\:{x}−{e}\mathrm{ln}{x},\:{x}>\mathrm{0} \\ $$$${f}'\left({x}\right)\:=\:\mathrm{1}−\frac{{e}}{{x}} \\ $$$${f}'\left({x}\right)\:=\:\mathrm{0}\:\Leftrightarrow\:{x}\:=\:{e} \\ $$$${f}\left({e}\right)\:=\:{e}−{e}\mathrm{ln}{e}\:=\:{e}−{e}\:=\:\mathrm{0} \\ $$$$\left.\mathrm{And}\:\mathrm{for}\:{x}\in\right]{e};+\infty\left[\:{f}'\left({x}\right)>\mathrm{0}\right.…
Question Number 102231 by Tinku Tara last updated on 07/Jul/20 $$\mathrm{Tutorial}\:\mathrm{video}\:\mathrm{for}\:\mathrm{using}\:\mathrm{shape} \\ $$$$\mathrm{and}\:\mathrm{drawing}\:\mathrm{tools} \\ $$ Commented by Tinku Tara last updated on 07/Jul/20 https://youtu.be/khu95JONx_A Commented…
Question Number 102204 by Tinku Tara last updated on 07/Jul/20 $$\mathrm{New}\:\mathrm{updates}: \\ $$$$\centerdot\:\mathrm{You}\:\mathrm{can}\:\mathrm{save}/\mathrm{load}\:\mathrm{equation}\:\mathrm{in}\:\mathrm{a}\:\mathrm{file} \\ $$$$\:\:\:\mathrm{and}\:\mathrm{edit}\:\mathrm{it}\:\mathrm{again}. \\ $$$$\:\:\:\mathrm{This}\:\mathrm{enables}\:\mathrm{sharing}\:\mathrm{of}\:\mathrm{editable} \\ $$$$\:\:\:\:\mathrm{equation}. \\ $$$$\centerdot\:\:\mathrm{New}\:\mathrm{symbols}\:\mathrm{added} \\ $$$$\centerdot\:\:\:\mathrm{A}\:\mathrm{few}\:\mathrm{bug}\:\mathrm{fixes}. \\ $$$$\mathrm{v2}.\mathrm{093}.…
Question Number 167739 by DAVONG last updated on 24/Mar/22 Commented by mkam last updated on 24/Mar/22 $$−\infty \\ $$ Commented by mkam last updated on…
Question Number 102196 by mathocean1 last updated on 07/Jul/20 $${ABCD}\:{is}\:{a}\:{square}\:{with}\:{center}\:{O}. \\ $$$${AB}=\mathrm{5}\:{cm}. \\ $$$${EFGH}\:{is}\:{a}\:{square}\:{such}\:{as}\: \\ $$$${AE}={BF}={CG}={DH}. \\ $$$$\left.\mathrm{1}\right)\:{Show}\:{with}\:{Chasles}\:{rules}\:{that} \\ $$$$\overset{\rightarrow} {{EF}}.\overset{\rightarrow} {{FG}}=\overset{\rightarrow} {\mathrm{0}} \\ $$$$\left.\mathrm{2}\right)\:{Determinate}\:{the}\:{area}\:{of}\:{EBFO}…
Question Number 167696 by bounhome last updated on 23/Mar/22 $${solv}:\:\: \\ $$$${e}^{{x}} +{x}+\mathrm{1}=\mathrm{0} \\ $$ Answered by mr W last updated on 23/Mar/22 $${e}^{{x}} =−\left({x}+\mathrm{1}\right)…
Question Number 167682 by bounhome last updated on 22/Mar/22 $${solve}:\:\mathrm{2}^{{x}} +\mathrm{3}^{{x}} =\mathrm{5}^{{x}} \\ $$ Commented by mr W last updated on 22/Mar/22 $${is}\:{it}\:{not}\:{to}\:{see}\:{that}\:{x}=\mathrm{1}? \\ $$…
Question Number 102146 by MJS last updated on 06/Jul/20 $$\mathrm{I}\:\mathrm{decided}\:\mathrm{it}'\mathrm{s}\:\mathrm{time}\:\mathrm{to}\:\mathrm{leave}\:\mathrm{for}\:\mathrm{a}\:\mathrm{while}.\:\mathrm{I}\:\mathrm{need} \\ $$$$\mathrm{some}\:\mathrm{peace}\:\mathrm{and}\:\mathrm{calm},\:\mathrm{I}'\mathrm{m}\:\mathrm{losing}\:\mathrm{my}\:{zen}\mathrm{ter}… \\ $$$$\mathrm{I}'\mathrm{ll}\:\mathrm{put}\:\mathrm{more}\:\mathrm{time}\:\mathrm{and}\:\mathrm{energy}\:\mathrm{into}\:\mathrm{my}\:\mathrm{music}. \\ $$$$\mathrm{I}\:\mathrm{guess}\:\mathrm{I}'\mathrm{ll}\:\mathrm{be}\:\mathrm{back};\:\mathrm{until}\:\mathrm{then}, \\ $$$$\mathrm{kindest}\:\mathrm{regards}\:\&\:\mathrm{thanks}\:\mathrm{for}\:\mathrm{the}\:\mathrm{teachings}! \\ $$ Commented by Rasheed.Sindhi last updated…
Question Number 102139 by mathocean1 last updated on 06/Jul/20 $${We}\:{have}\:\mathrm{4}\:{boys}\:{and}\:\mathrm{2}\:{girls}.\:{we} \\ $$$${choose}\:{at}\:{random}\:{and}\:{simultaneous} \\ $$$$\mathrm{2}\:{boys}\:{and}\:\mathrm{1}\:{girl}\:{to}\:{for}\:{a}\:{group}. \\ $$$$\left.\mathrm{1}\right)\:{How}\:{many}\:{possibilities}\:{do}\:{we}\:{have}? \\ $$ Commented by prakash jain last updated on…
Question Number 167666 by LEKOUMA last updated on 22/Mar/22 $${I}_{{n}} =\int\frac{{dx}}{\mathrm{cos}\:^{{n}} {x}} \\ $$$${Prove}\:{that} \\ $$$${I}_{{n}} =\frac{{n}−\mathrm{2}}{{n}−\mathrm{1}}{I}_{{n}−\mathrm{2}} +\frac{\mathrm{sin}\:{x}}{\left({n}−\mathrm{1}\right)\mathrm{cos}\:^{{n}−\mathrm{1}} {x}} \\ $$ Commented by peter frank…