Question Number 208421 by lepuissantcedricjunior last updated on 15/Jun/24 Commented by Frix last updated on 15/Jun/24 $$\Psi=\mathrm{2}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{tan}\:\mathrm{2}{x}}}\:\overset{{t}=\sqrt{\mathrm{tan}\:\mathrm{2}{x}}} {=}\:\mathrm{2}\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dt}}{{t}^{\mathrm{4}} +\mathrm{1}}=\frac{\sqrt{\mathrm{2}}\pi}{\mathrm{2}} \\ $$…
Question Number 208423 by lepuissantcedricjunior last updated on 15/Jun/24 $$\:\:\:\boldsymbol{{calculons}}\: \\ $$$$\boldsymbol{{i}}=\int\int\int_{\left[\mathrm{0};\mathrm{1}\right]} \frac{\boldsymbol{{dxdydz}}}{\mathrm{1}−\boldsymbol{{xyz}}} \\ $$ Answered by Berbere last updated on 15/Jun/24 $$=\int\int\left[−\frac{\mathrm{1}}{{xy}}{ln}\left(\mathrm{1}−{xy}\right)\right]{dydx} \\ $$$${xy}={u}\Rightarrow{dy}=\frac{{du}}{{x}}…
Question Number 208418 by alcohol last updated on 16/Jun/24 $$\left.{u}_{{n}+\mathrm{1}} \:=\:{u}_{{n}} −{u}_{{n}} ^{\mathrm{3}} \:;\:{u}_{\mathrm{0}} \:\in\:\right]\mathrm{0},\:\mathrm{1}\left[\right. \\ $$$$\left..\:{show}\:{that}\:{u}_{{n}} \:\in\:\right]\mathrm{0},\:\mathrm{1}\left[\right. \\ $$$$.\:{show}\:{that}\:{u}_{{n}} \:{converges}\:{to}\:\mathrm{0} \\ $$$${v}_{{n}} \:=\:\frac{\mathrm{1}}{{u}_{{n}+\mathrm{1}} ^{\mathrm{2}}…
Question Number 208381 by hardmath last updated on 14/Jun/24 $$\mathrm{g}\left(\mathrm{x}\right)\:=\:\mathrm{lnx}^{\mathrm{2}} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:+\:\mathrm{25}} \\ $$$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\boldsymbol{\mathrm{e}}} {\mathrm{lim}}\:\left(\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)\:=\:?\right. \\ $$ Answered by A5T last updated on 14/Jun/24 $${f}\left({g}\left({x}\right)\right)=\sqrt[{\mathrm{3}}]{{ln}\left({x}^{\mathrm{2}}…
Question Number 208398 by mokys last updated on 14/Jun/24 $${write}\:{z}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}+{i}}\:{in}\:{e}^{{i}\theta} \\ $$ Answered by A5T last updated on 14/Jun/24 $${z}=\frac{\sqrt{\mathrm{3}}−{i}}{\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} −\left({i}\right)^{\mathrm{2}} }=\frac{\sqrt{\mathrm{3}}−{i}}{\mathrm{4}},\:\mid{z}\mid=\sqrt{\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}\right)^{\mathrm{2}} +\left(\frac{−\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{4}} \\…
Question Number 208377 by hardmath last updated on 14/Jun/24 $$\mathrm{sin}\:\mathrm{x}\:−\:\mathrm{sin}\:\frac{\pi}{\mathrm{6}}\:>\:\mathrm{0} \\ $$$$\mathrm{x}\:=\:? \\ $$ Commented by hardmath last updated on 14/Jun/24 $$ \\ $$Solve the…
Question Number 208395 by efronzo1 last updated on 14/Jun/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 208384 by efronzo1 last updated on 14/Jun/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by A5T last updated on 14/Jun/24 $${log}_{{abc}} \left({a}\right)+{log}_{{abc}} \left({b}\right)=\mathrm{2}+\mathrm{3}=\mathrm{5}\Rightarrow{log}_{{abc}} \left({ab}\right)=\mathrm{5} \\ $$$${log}_{{abc}}…
Question Number 208385 by efronzo1 last updated on 14/Jun/24 Commented by efronzo1 last updated on 15/Jun/24 Commented by efronzo1 last updated on 15/Jun/24 $$\mathrm{i}'\mathrm{m}\:\mathrm{stuck}\:\mathrm{this}\:\mathrm{step} \\…
Question Number 208370 by lmcp1203 last updated on 14/Jun/24 $${if}\:\:\:\left({fof}\right)\left({x}\right)={f}\left({x}\right)+{x}\:\:{and}\:{f}\left(\mathrm{1}\right)=\mathrm{1}\:\:\: \\ $$$${find}\:\:{fofofofofofofofofof}\left(\mathrm{1}\right) \\ $$ Commented by A5T last updated on 14/Jun/24 $${f}\left({f}\left({x}\right)\right)={f}\left({x}\right)+{x}\Rightarrow\:{f}\left({f}\left(\mathrm{1}\right)\right)={f}\left(\mathrm{1}\right)+\mathrm{1} \\ $$$$\Rightarrow{f}\left(\mathrm{1}\right)={f}\left(\mathrm{1}\right)+\mathrm{1}\Rightarrow\mathrm{1}\overset{?} {=}\mathrm{0}…