Question Number 198001 by mathlove last updated on 07/Oct/23 $$\int\left({e}\right)^{\left({x}\right)^{{lnx}} } \:{dx}=? \\ $$ Commented by Frix last updated on 07/Oct/23 $$\left(\mathrm{e}\right)^{\left({x}\right)^{\mathrm{ln}\:{x}} } =\mathrm{e}^{\left({x}^{\mathrm{ln}\:{x}} \right)}…
Question Number 197998 by mathlove last updated on 07/Oct/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{{x}^{\mathrm{3}} }=? \\ $$$${with}\:{out}\:{L}'{Hospital}\:{rul} \\ $$ Answered by witcher3 last updated on 07/Oct/23 $$\mathrm{x}=\mathrm{sh}\left(\mathrm{t}\right),\mathrm{t}\rightarrow\mathrm{0}…
Question Number 197989 by mr W last updated on 07/Oct/23 Commented by mr W last updated on 07/Oct/23 $$\left[\underline{{old}\:{question}\:{from}\:{ajfour}\:{sir}}\right] \\ $$$$\mathrm{3}\:{circles}\:{with}\:{radii}\:{p},\:{q},\:{r}\:{respectively} \\ $$$${touch}\:{each}\:{other}\:{as}\:{shown}.\:{find}\:{the}\: \\ $$$${maximum}\:{area}\:{of}\:\:{triangle}\:\Delta{ABC}…
Question Number 197985 by mokys last updated on 07/Oct/23 $$\underset{{n}\rightarrow\infty} {{lim}}\:\left(\underset{\:{k}} {\overset{\:\:{n}} {\:}}\:\right)\:{p}^{{k}} \:{q}^{{n}−{k}} \\ $$ Commented by mr W last updated on 07/Oct/23 $${question}\:{in}\:{current}\:{form}\:{makes}\:{no}…
Question Number 198018 by obia last updated on 07/Oct/23 Answered by a.lgnaoui last updated on 08/Oct/23 $$\boldsymbol{\mathrm{Z}}=\sqrt{\mathrm{3}}\:+\mathrm{1}+\:\boldsymbol{\mathrm{i}}\left(\sqrt{\mathrm{3}}\:−\mathrm{1}\right) \\ $$$$ \\ $$$$\left.\bullet\mathrm{1}\right):\:\:\boldsymbol{\mathrm{Z}}^{\mathrm{2}} =\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}}\:\:−\left(\mathrm{4}−\mathrm{2}\sqrt{\mathrm{3}}\:\right)+\mathrm{2}\boldsymbol{\mathrm{i}}\left(\sqrt{\mathrm{3}}\:+\mathrm{1}\right)\left(\sqrt{\mathrm{3}}\:−\:\mathrm{1}\right) \\ $$$$\:\:\:=\mathrm{4}\sqrt{\mathrm{3}}\:\:+\mathrm{4}\boldsymbol{\mathrm{i}}\:\:=\mathrm{4}\left(\sqrt{\mathrm{3}}\:+\boldsymbol{\mathrm{i}}\right) \\…
Question Number 197967 by Blackpanther last updated on 06/Oct/23 Answered by mr W last updated on 06/Oct/23 $${f}\left({x}\right)={a}\left({x}+\mathrm{1}\right)\left({x}−\mathrm{10}\right) \\ $$$$\frac{\mathrm{20}}{\mathrm{3}}={a}\left(\mathrm{0}+\mathrm{1}\right)\left(\mathrm{0}−\mathrm{10}\right) \\ $$$$\Rightarrow{a}=−\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${at}\:{x}=\frac{−\mathrm{1}+\mathrm{10}}{\mathrm{2}}=\frac{\mathrm{9}}{\mathrm{2}}: \\…
Question Number 197960 by a.lgnaoui last updated on 06/Oct/23 $$\mathrm{determiner}\:\mathrm{le}\:\mathrm{total}\:\mathrm{de}\:\mathrm{nombres}\:\mathrm{de}\: \\ $$$$\mathrm{5}\:\mathrm{chiffres}\:\mathrm{comprises}\:\mathrm{entre}\:\mathrm{10000}\:\mathrm{et}\: \\ $$$$\mathrm{50000}\:\:\mathrm{divisibles}\:\mathrm{simultanement}\:\mathrm{par} \\ $$$$\mathrm{5}\:\mathrm{et}\:\mathrm{9}\:\:\: \\ $$$$\left(\mathrm{sans}\:\mathrm{utiliser}\:\mathrm{les}\:\mathrm{formules}\:\mathrm{d}\:\mathrm{arrangement}\right. \\ $$$$\left.\mathrm{et}\:\mathrm{de}\:\mathrm{combinaison}\right) \\ $$$$ \\ $$ Answered…
Question Number 197961 by cherokeesay last updated on 06/Oct/23 $$ \\ $$A cylindrical container is designed to contain bees. At exactly 12:00pm, there are 2…
Question Number 197972 by mnjuly1970 last updated on 07/Oct/23 $$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{Find}\: \\ $$$$\:\:\:\:\:\:\:\mathscr{L}\:^{−\mathrm{1}} \left\{\:\:\frac{\mathrm{1}}{\mathrm{2}^{\:{s}} \:\sqrt{\:\mathrm{2}{s}+\mathrm{1}}\:}\:\right\}=\:? \\ $$$$ \\ $$$$\:\:\:\:\:\:{inverse}\:\:{laplace}\:{transform}… \\ $$ Terms of Service…
Question Number 197970 by mr W last updated on 06/Oct/23 Answered by Frix last updated on 07/Oct/23 $${r}_{\mathrm{1}} =\mathrm{4} \\ $$$${r}_{\mathrm{2}} =\mathrm{2} \\ $$$${r}_{\mathrm{3}} =\mathrm{1}…