Question Number 130541 by EDWIN88 last updated on 26/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{−{x}^{\mathrm{2}} /\mathrm{2}} −\mathrm{cos}\:{x}}{{x}^{\mathrm{3}} \:\mathrm{tan}\:{x}}\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 65004 by mathmax by abdo last updated on 24/Jul/19 $${let}\:{U}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{\frac{\mathrm{2}}{{n}}} \:\Gamma\left({x}\right)\Gamma\left(\mathrm{1}−{x}\right){dx}\:\:\:\:{with}\:{n}\geqslant\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{and}\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by mathmax…
Question Number 65003 by mathmax by abdo last updated on 24/Jul/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\Gamma\left({x}\right)}\:\:{with}\:\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\:\:\left({x}>\mathrm{0}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 130536 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)\mathrm{d}\theta \\ $$ Answered by Ar Brandon last updated on 26/Jan/21…
Question Number 130537 by benjo_mathlover last updated on 26/Jan/21 Answered by EDWIN88 last updated on 26/Jan/21 $$\Leftrightarrow\:\overset{\rightarrow} {{a}}×\left(\overset{\rightarrow} {{b}}×\overset{\rightarrow} {{c}}\right)=\left(\overset{\rightarrow} {{a}}.\overset{\rightarrow} {{c}}\right)\overset{\rightarrow} {{b}}−\left(\overset{\rightarrow} {{a}}.\overset{\rightarrow} {{b}}\right)\overset{\rightarrow}…
Question Number 130534 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{7}} \:\mathrm{arctan}\left(\mathrm{2x}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculate}\:\:\mathrm{f}^{\left(\mathrm{4}\right)} \left(\mathrm{0}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{7}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{5}\right)} \left(\mathrm{1}\right) \\ $$ Answered by mathmax…
Question Number 130535 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{n}} \:\mathrm{e}^{−\mathrm{nx}} \mathrm{arctan}\left(\mathrm{nx}+\mathrm{2}\right) \\ $$$$\mathrm{calculate}\:\mathrm{g}^{\left(\mathrm{n}\right)} \left(\mathrm{o}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 130532 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{find}\:\mathrm{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{1}+\alpha\mathrm{x}\right)}{\mathrm{4}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\:\left(\alpha>\mathrm{0}\right) \\ $$$$\mathrm{and}\:\mathrm{determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{1}+\mathrm{2x}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}}\mathrm{dx} \\ $$ Terms of Service…
Question Number 130533 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{find}\:\int\:\:\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{5}}{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{2}} −\mathrm{3}}\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21…
Question Number 130530 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{xsin}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated…