Question Number 196522 by Erico last updated on 26/Aug/23 $$\mathrm{Prove}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N} \\ $$$$\underset{\:\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} \mathrm{ln}{t}\:\mathrm{dt}\:\leqslant\:\mathrm{ln}\left(\underset{\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} {t}\:\mathrm{dt}\right) \\ $$ Answered by aleks041103 last updated on 26/Aug/23…
Question Number 196490 by tri26112004 last updated on 26/Aug/23 $${Know}:\:{xf}\left({x}\right)−{f}'\left({x}\right)={x}^{\mathrm{2}} \\ $$$${Find}\:{f}\left({x}\right)=¿ \\ $$ Commented by mr W last updated on 26/Aug/23 $${i}\:{have}\:{given}\:{you}\:{the}\:{answer}\:{in}\: \\ $$$${Q}\mathrm{196398}.\:{you}\:{didn}'{t}\:{show}\:{any}\:{response}…
Question Number 196517 by ERLY last updated on 26/Aug/23 Answered by mr W last updated on 27/Aug/23 $$\mathrm{cos}\:{x}+{i}\:\mathrm{sin}\:{x}={e}^{{ix}} \\ $$$$\mathrm{cos}\:{x}−{i}\:\mathrm{sin}\:{x}={e}^{−{ix}} \\ $$$$\Rightarrow\mathrm{cos}\:{x}=\frac{{e}^{{ix}} +{e}^{−{ix}} }{\mathrm{2}}=\mathrm{2} \\…
Question Number 196516 by SANOGO last updated on 26/Aug/23 Answered by witcher3 last updated on 27/Aug/23 $$\mathrm{Quelle}\:\mathrm{Question}\:? \\ $$$$\mathrm{ex3}\:\mathrm{Th}\:\mathrm{cv}\:\mathrm{Domine} \\ $$$$\mathrm{Exo}\:\mathrm{4}\:\mathrm{defintion}\:\mathrm{de}\:\mathrm{tribue}\:\mathrm{Engendrd};\:\mathrm{fonction}\:\mathrm{mesurable} \\ $$ Terms of…
Question Number 196519 by mr W last updated on 26/Aug/23 $${if}\:{xyz}=\mathrm{1},\:{prove} \\ $$$$\left(\frac{{x}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{y}}{{y}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{z}}{{z}−\mathrm{1}}\right)^{\mathrm{2}} \geqslant\mathrm{1}. \\ $$ Answered by mahdipoor last updated on 27/Aug/23…
Question Number 196518 by ERLY last updated on 26/Aug/23 $${resouxre}\:{cosx}=\mathrm{2} \\ $$ Answered by Frix last updated on 26/Aug/23 $$\mathrm{Similar}\:\mathrm{to}\:\mathrm{the}\:\mathrm{other}\:\mathrm{question} \\ $$$${x}=\mathrm{2}{n}\pi\pm\mathrm{i}\:\mathrm{ln}\:\left(\mathrm{2}+\sqrt{\mathrm{3}}\right) \\ $$ Terms…
Question Number 196515 by hardmath last updated on 26/Aug/23 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:+\infty} \:\mathrm{x}^{\boldsymbol{\pi}} \:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$ Answered by aleks041103 last updated on 26/Aug/23 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 196447 by cortano12 last updated on 25/Aug/23 $$\:\:\:\:\mathrm{n}!\:=\:\mathrm{2}^{\mathrm{25}} ×\mathrm{3}^{\mathrm{13}} ×\mathrm{5}^{\mathrm{6}} ×\mathrm{7}^{\mathrm{4}} ×\mathrm{11}^{\mathrm{2}} ×\mathrm{13}^{\mathrm{2}} ×\mathrm{17}×\mathrm{19}×\mathrm{23} \\ $$$$\:\:\:\mathrm{n}=? \\ $$ Answered by Frix last updated…
Question Number 196471 by Tawa11 last updated on 25/Aug/23 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}}\left(\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{n}}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{2}}{\mathrm{n}}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{3}}{\mathrm{n}}}\:\:+\:\:..\:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{n}}{\mathrm{n}}}\right) \\ $$ Answered by mr W last updated on 25/Aug/23 $$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\mathrm{2}+{x}} \\…
Question Number 196464 by mokys last updated on 25/Aug/23 $${if}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} +{x}^{\mathrm{2}} \:\:,\:{g}\left({x}\right)=\:{f}^{−\mathrm{1}} \left({x}\right)\:,\:{find}\:{g}^{'} \left(\mathrm{3}\right)\:?\:\: \\ $$ Answered by Frix last updated on 25/Aug/23 $${y}={x}^{\mathrm{3}} +{x}^{\mathrm{2}}…