Question Number 73487 by abdomathmax last updated on 13/Nov/19 $${let}\:\:\:\:\alpha\:{and}\:\beta\:{roots}\:{of}\:\:{the}\:{equation}\:\:{x}^{\mathrm{2}} −{x}+\mathrm{2}=\mathrm{0} \\ $$$${simplify}\:\:\:{A}_{{p}} =\:\alpha^{{p}} \:+\beta^{{p}} \:{and}\:{calculate} \\ $$$$\sum_{{p}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{A}_{{p}} \:\:{and}\:\sum_{{p}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{A}_{{p}} ^{\mathrm{2}} \\…
Question Number 73486 by abdomathmax last updated on 13/Nov/19 $${let}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\right)^{{n}} −\left(\mathrm{1}−{ix}\right)^{{n}} \:{with}\:{n}\:{integr} \\ $$$${decompose}\:{the}\:{Fraction}\:{F}\:\left({x}\right)=\frac{\mathrm{1}}{{P}\left({x}\right)} \\ $$ Commented by abdomathmax last updated on 17/Nov/19 $${P}\left({x}\right)=\mathrm{0}\:\Leftrightarrow\frac{\left(\mathrm{1}−{ix}\right)^{{n}} }{\left(\mathrm{1}+{ix}\right)^{{n}}…
Question Number 73485 by abdomathmax last updated on 13/Nov/19 $${find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\:+{jx}^{\mathrm{2}} \right)^{{n}} −\mathrm{1} \\ $$$${with}\:{j}\:={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{then}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$${decompose}\:{the}\:{fraction}\:{F}=\frac{\mathrm{1}}{{P}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 73473 by mathmax by abdo last updated on 13/Nov/19 $${let}\:{z}\:{from}\:{C}\:{prove}\:{that}\: \\ $$$${arcsinz}=−{iln}\left({iz}+\sqrt{\mathrm{1}−{z}^{\mathrm{2}} }\right) \\ $$$${arccosz}\:=−{iln}\left({z}+\sqrt{{z}^{\mathrm{2}} −\mathrm{1}}\right) \\ $$ Commented by mathmax by abdo…
Question Number 73411 by mathmax by abdo last updated on 11/Nov/19 $${calculate}\:\: \\ $$$$\left.\mathrm{1}\right){cos}\left(\mathrm{1}+{i}\right)\:,\:{sin}\left(\mathrm{1}+\mathrm{3}{i}\right) \\ $$$$\left.\mathrm{2}\right)\:{arctan}\left({i}\right),\:{arctan}\left(\mathrm{2}{i}\right)\:,\:{arctan}\left(\mathrm{1}+{i}\right)\:,{arctan}\left(\mathrm{1}−{i}\right)\:, \\ $$$${arctan}\left(\mathrm{1}+\mathrm{2}{i}\right). \\ $$$$\left.\mathrm{3}\right)\:{have}\:{us}\:\:{conj}\left({arctanz}\right)={arctan}\left(\overset{−} {{z}}\right)? \\ $$ Commented by…
Question Number 73396 by mathmax by abdo last updated on 11/Nov/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{t}^{\mathrm{2}} } {ln}\left(\mathrm{1}−{t}\right){dt} \\ $$ Commented by mathmax by abdo last updated…
Question Number 7833 by mohitkumar88@gmail.com last updated on 18/Sep/16 $$\mathrm{3}\frac{\mathrm{3}}{\mathrm{4}}×\mathrm{2}\frac{\mathrm{2}}{\mathrm{3}}= \\ $$ Answered by Rasheed Soomro last updated on 18/Sep/16 $$\mathrm{3}\frac{\mathrm{3}}{\mathrm{4}}×\mathrm{2}\frac{\mathrm{2}}{\mathrm{3}}=\frac{\overset{\mathrm{5}} {\mathrm{15}}}{\underset{\mathrm{1}} {\mathrm{4}}}×\frac{\overset{\mathrm{2}} {\mathrm{8}}}{\underset{\mathrm{1}} {\mathrm{3}}}=\frac{\mathrm{10}}{\mathrm{1}}=\mathrm{10}…
Question Number 73334 by mathmax by abdo last updated on 10/Nov/19 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:{n}^{\mathrm{2}} \left(\:{e}^{{sin}\left(\frac{\pi}{{n}^{\mathrm{2}} }\right)} −{cos}\left(\frac{\pi}{{n}}\right)\right) \\ $$ Answered by Smail last updated on 10/Nov/19…
Question Number 73332 by mathmax by abdo last updated on 10/Nov/19 $${let}\:{U}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\:\sqrt{\mathrm{2}{k}+\mathrm{1}}}\:\:{determine}\:{a}\:{equivalent}\:{of}\:{n}\:{when}\:{n}\rightarrow+\infty \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73327 by mathmax by abdo last updated on 10/Nov/19 $${let}\:{w}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{explicit}\:{w}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnt}}{\left({n}^{\mathrm{2}} \:+{t}^{\mathrm{2}}…