Question Number 5153 by 1771727373 last updated on 23/Apr/16 $${proof}\:\:\:\:{e}^{{i}\Theta} ={cos}\left(\Theta\right)+{isin}\left(\Theta\right) \\ $$ Answered by 123456 last updated on 23/Apr/16 $$\mathrm{lets}\:{f}\left(\theta\right)=\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta,{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$$\frac{\partial{f}}{\partial\theta}=−\mathrm{sin}\:\theta+{i}\mathrm{cos}\:\theta={i}\left(\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta\right)={if} \\ $$$$\frac{{df}}{{f}}={id}\theta…
Question Number 5152 by 1771727373 last updated on 23/Apr/16 $${there}\:{is}\:{an}\:{ineterger}\:{a},{b},{c} \\ $$$${can}\:{there}\:{be}\:{an}\:{interger}\:{as}\: \\ $$$${a}^{{n}} +{b}^{{n}+\mathrm{1}} ={c}^{{n}+\mathrm{2}} \:\:\:\:\:\:\left({n}\:{is}\:{a}\:{interger}\right) \\ $$$$ \\ $$ Commented by Yozzii last…
Question Number 70686 by mathmax by abdo last updated on 06/Oct/19 $${find}\:\int\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{6}} } \\ $$ Answered by kaivan.ahmadi last updated on 06/Oct/19 Answered by MJS…
Question Number 5150 by FilupSmith last updated on 21/Apr/16 $$\mathrm{If}\:\mathrm{we}\:\mathrm{had}\:\mathrm{a}\:\mathrm{maze},\:\mathrm{which}\:\mathrm{was}\:\mathrm{contained} \\ $$$$\mathrm{within}\:\mathrm{the}\:\mathrm{shape}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square},\:\mathrm{and}\:\mathrm{it}\:\mathrm{has} \\ $$$$\mathrm{one}\:\mathrm{enterence}\:\mathrm{on}\:\mathrm{its}\:\mathrm{edge},\:\mathrm{and}\:\mathrm{a}\:\mathrm{centre} \\ $$$$\mathrm{point}\:\mathrm{from}\:\mathrm{which}\:\mathrm{you}\:\mathrm{start},\:\mathrm{If}\:\mathrm{you}\:\mathrm{move} \\ $$$$\mathrm{randomly},\:\mathrm{you}\:\mathrm{will}\:\mathrm{naturally}\:\mathrm{escape}. \\ $$$$ \\ $$$$\mathrm{Now},\:\mathrm{lets}\:\mathrm{say}\:\mathrm{the}\:\mathrm{maze}\:\mathrm{itself}\:\mathrm{is}\:\mathrm{generated} \\ $$$$\mathrm{at}\:\mathrm{completely}\:\mathrm{random}\:\mathrm{odds}. \\…
Question Number 5144 by Yozzii last updated on 19/Apr/16 $${Let}\:{n},{j},{q}\in\left(\mathbb{Z}^{+} −\left\{\mathrm{1}\right\}\right).\:{Are}\:{there}\: \\ $$$${triples}\:\left({n},{j},{q}\right)\:{such}\:{that}\:{the}\:{following} \\ $$$${conditions}\:{are}\:{satisfied}\:{altogether}? \\ $$$$\left({i}\right)\:{n}={j}^{{q}} \:\:\:\: \\ $$$$\left({ii}\right){n}^{\mathrm{2}} ={j}^{\mathrm{2}} +{q}^{\mathrm{2}} \\ $$$$−−−−−−−−−−−−−−−−−−−−−− \\…
Question Number 70679 by cesar.marval.larez@gmail.com last updated on 06/Oct/19 $${Hi},\:{i}\:{wanna}\:{learn}\:{more}\:{english}. \\ $$$${can}\:{someone}\:{help}\:{me}? \\ $$$${write}\:{please}\:+\mathrm{584249229498} \\ $$ Commented by mr W last updated on 07/Oct/19 $${here}\:{is}\:{definitively}\:{not}\:{the}\:{best}\:{place}\:{to}…
Question Number 136209 by SOMEDAVONG last updated on 19/Mar/21 $$\left.\mathrm{1}\right).\int\sqrt{\mathrm{tanx}}\mathrm{dx}=? \\ $$ Answered by Ar Brandon last updated on 19/Mar/21 $$\mathrm{Q113706} \\ $$ Answered by…
Question Number 136211 by greg_ed last updated on 19/Mar/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{guyz}}\:!\: \\ $$$$\boldsymbol{\mathrm{please}},\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{ur}}\:\boldsymbol{\mathrm{help}}\:! \\ $$$$\boldsymbol{\mathrm{I}}=\int_{\mathrm{1}} ^{\:\mathrm{5}} \boldsymbol{{xe}}^{\boldsymbol{{x}}^{\mathrm{3}} } \boldsymbol{{dx}} \\ $$ Answered by Olaf last updated…
Question Number 70672 by ajfour last updated on 06/Oct/19 Commented by ajfour last updated on 06/Oct/19 $${Find}\:{sides}\:{of}\:\bigtriangleup{ABC}.\:{Also}\:{find} \\ $$$$\:{the}\:{same}\:{if}\:{instead}\:{of}\:{EF}\:, \\ $$$$\:{DF}=\mathrm{2}\:. \\ $$ Answered by…
Question Number 136210 by Ar Brandon last updated on 19/Mar/21 $$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{lnx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx}=−\frac{\pi}{\mathrm{4}} \\ $$ Commented by Ar Brandon last updated on 19/Mar/21…