Question Number 142176 by malwaan last updated on 27/May/21 $$\int\:{e}^{{ax}} \:{sin}\:{bx}\:{dx}\:=\:? \\ $$ Answered by Dwaipayan Shikari last updated on 27/May/21 $${sin}\left({bx}\right)=\frac{{e}^{{ibx}} −{e}^{−{ibx}} }{\mathrm{2}{i}} \\…
Question Number 11101 by FilupS last updated on 12/Mar/17 Commented by FilupS last updated on 12/Mar/17 $$\mathrm{assume}\:\mathrm{that}\:\mathrm{any}\:\mathrm{drawn}\:\mathrm{cards}\:\mathrm{are}\:\mathrm{not} \\ $$$$\mathrm{returned} \\ $$ Answered by DrDaveR last…
Question Number 142174 by mohammad17 last updated on 27/May/21 Commented by mohammad17 last updated on 27/May/21 $$????????? \\ $$ Commented by MJS_new last updated on…
Question Number 142168 by iloveisrael last updated on 27/May/21 Commented by liberty last updated on 27/May/21 $$=\:\mathrm{19} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 142171 by iloveisrael last updated on 27/May/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left(\mathrm{1}−\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{\mathrm{sin}\:^{\mathrm{3}} {x}−\mathrm{tan}\:^{\mathrm{3}} {x}}\:=? \\ $$ Answered by iloveisrael last updated on 27/May/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left(\mathrm{2sin}\:^{\mathrm{2}}…
Question Number 76633 by mathmax by abdo last updated on 28/Dec/19 $${calculate}\:{cos}^{\mathrm{6}} \left(\frac{\pi}{\mathrm{8}}\right)+{cos}^{\mathrm{6}} \left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)+{cos}^{\mathrm{6}} \left(\frac{\mathrm{5}\pi}{\mathrm{8}}\right)+{cos}^{\mathrm{6}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}\right) \\ $$ Answered by MJS last updated on 28/Dec/19…
Question Number 76630 by Rio Michael last updated on 28/Dec/19 $$\mathrm{two}\:\mathrm{sequences}\:,\:\left({u}_{{n}} \right)\:{and}\:\left({v}_{{n}} \right),\:\mathrm{for}\:{n}\in\mathbb{N}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as}: \\ $$$$\begin{cases}{{u}_{\mathrm{0}} \:=\mathrm{3}}\\{{u}_{{n}+\mathrm{1}} =\:\frac{\mathrm{1}}{\mathrm{2}}\left({u}_{{n}} \:+\:{v}_{{n}} \right)\:\:}\end{cases}\mathrm{and}\:\begin{cases}{{v}_{\mathrm{0}} =\:\mathrm{4}}\\{{v}_{{n}+\mathrm{1}} =\:\frac{\mathrm{1}}{\mathrm{2}}\left({u}_{{n}+\mathrm{1}} \:+\:{v}_{{n}} \right)}\end{cases} \\ $$$$\left.{a}\right)\:\mathrm{calculate}\:{u}_{\mathrm{1}}…
Question Number 11095 by FilupS last updated on 12/Mar/17 $$\mathrm{You}\:\mathrm{have}\:\mathrm{a}\:\mathrm{line}\:\mathrm{of}\:\mathrm{length}\:\mathrm{1}. \\ $$$$\mathrm{You}\:\mathrm{place}\:\mathrm{two}\:\mathrm{random}\:\mathrm{points}\:\mathrm{on}\:\mathrm{the}\:\mathrm{line}. \\ $$$$\: \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{average}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{points}?\:\mathrm{Please}\:\mathrm{show}\:\mathrm{your}\:\mathrm{working}. \\ $$ Commented by FilupS last updated…
Question Number 142164 by Panacea last updated on 27/May/21 Commented by Panacea last updated on 27/May/21 $${plse}\:{sol} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 142167 by iloveisrael last updated on 27/May/21 $$\:\:\:{Find}\:{max}\:\&\:{min}\:{of}\:{function} \\ $$$$\:\:{f}\left({x}\right)=\mathrm{4tan}\:{x}+\mathrm{3cot}\:{x} \\ $$ Answered by MJS_new last updated on 27/May/21 $$−\infty<\mathrm{tan}\:{x}\:<+\infty\:\Rightarrow\:\mathrm{no}\:\mathrm{absolute}\:\mathrm{min},\:\mathrm{max} \\ $$$${g}\left({t}\right)=\mathrm{4}{t}+\frac{\mathrm{3}}{{t}} \\…