Question Number 98244 by ~blr237~ last updated on 12/Jun/20 $$\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:{xe}^{{cosx}} {cos}\left({sinx}\right){dx}=\:\mathrm{2}\pi^{\mathrm{2}} \\ $$ Answered by maths mind last updated on 15/Jun/20 $${e}^{{cos}\left({x}\right)+{isin}\left({x}\right)} ={e}^{{cos}\left({x}\right)}…
Question Number 98213 by me2love2math last updated on 12/Jun/20 Commented by bemath last updated on 12/Jun/20 $$\mathrm{let}\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{t}\:,\:\mathrm{t}\:\rightarrow\mathrm{0}\: \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{3}{t}\right)}{{t}}\:=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{3}}{\mathrm{1}+\mathrm{3t}}}{\mathrm{1}}\:=\:\frac{\mathrm{3}}{\mathrm{1}}=\mathrm{3} \\ $$ Answered by…
Question Number 163732 by mnjuly1970 last updated on 09/Jan/22 $$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{I}{f}\:,\:\:\boldsymbol{\phi}\:=\:\int_{−\infty} ^{\:+\infty} \frac{\:{sin}\left({x}\right).{ln}^{\:\mathrm{2}} \left({x}\:\right)}{{x}}\:\:{then} \\ $$$$\:\:\:\:\:\:{find}\:\::\:\:\:\:\:\:\:\:\:\mathcal{I}{m}\:\left(\boldsymbol{\phi}\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\: \\ $$$$ \\ $$ Terms of…
Question Number 163704 by mnjuly1970 last updated on 09/Jan/22 $$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{n}\left(\zeta\:\left(\mathrm{1}+{n}\right)\:−\mathrm{1}\right)\:=? \\ $$$$ \\ $$ Answered by Kamel last updated…
Question Number 163700 by blackmamba last updated on 09/Jan/22 $$\:\:\mathcal{K}\left({x}\right)\:=\:\frac{\mathrm{3}\:\mathrm{cos}\:{x}}{\mathrm{5}+\mathrm{4sin}\:{x}} \\ $$$$\:\left.\begin{matrix}{{max}\:\mathcal{K}\left({x}\right)}\\{{min}\:\mathcal{K}\left({x}\right)}\end{matrix}\right\}\:=? \\ $$ Answered by mr W last updated on 10/Jan/22 $$\frac{\mathrm{3}\:\mathrm{cos}\:{x}}{\mathrm{5}+\mathrm{4}\:\mathrm{sin}\:{x}}={k} \\ $$$$\mathrm{3}\:\mathrm{cos}\:{x}−\mathrm{4}{k}\:\mathrm{sin}\:{x}=\mathrm{5}{k}…
Question Number 163682 by mnjuly1970 last updated on 09/Jan/22 $$ \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\mathrm{Li}_{\:\mathrm{2}} ^{\:} \left({x}\:\right)\right)^{\:\mathrm{2}} {dx}\:=\:?\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\: \\ $$$$\:\:\:\:\:−−−\:−−− \\ $$$$\:\:\:\: \\ $$ Answered by…
Question Number 163613 by mnjuly1970 last updated on 08/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163533 by Ar Brandon last updated on 07/Jan/22 $$\mathrm{R}\acute {\mathrm{e}soudre}\:\:\:\:\:\:\frac{\partial^{\mathrm{2}} {u}}{\partial{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {u}}{\partial{y}^{\mathrm{2}} }={e}^{\mathrm{2}{x}+{y}} \\ $$ Commented by Rasheed.Sindhi last updated on 08/Jan/22…
Question Number 97972 by Aniruddha Ghosh last updated on 10/Jun/20 $$\:\:\:\:\mathrm{Prove}\:\mathrm{that}, \\ $$$$\:\:\:\:\:\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left(\boldsymbol{{e}}^{\boldsymbol{{x}}} \right)\:=\:\boldsymbol{{e}}^{\boldsymbol{{x}}} \\ $$ Answered by abdomathmax last updated on 10/Jun/20 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{e}^{\mathrm{x}} \right)\:=\mathrm{lim}_{\mathrm{h}\rightarrow\mathrm{0}}…
Question Number 163510 by mnjuly1970 last updated on 07/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\mathrm{I}{f} \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:\mathrm{1}}{\:\sqrt{{sin}^{\:\mathrm{5}} \left({x}\right).{cos}\left({x}\right)}\:+\sqrt{{cos}^{\:\mathrm{5}} \left({x}\right).{sin}\left({x}\right)}}{dx}\:= \\ $$$$\:\:\:{find}\:{the}\:{value}\:{of}\:\::\:\Gamma^{\:\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\:\right).\:\boldsymbol{\phi} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$…