Question Number 139024 by bramlexs22 last updated on 21/Apr/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\frac{\pi}{\mathrm{5}} \\ $$$$ \\ $$ Commented by EDWIN88 last updated on 21/Apr/21 $$\:\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{4}} \\ $$ Answered…
Question Number 73491 by abdomathmax last updated on 13/Nov/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:{e}^{−\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}} \:{dx} \\ $$ Commented by mathmax by abdo last updated on 14/Nov/19…
Question Number 139027 by mohammad17 last updated on 21/Apr/21 $${find}\:{Re}\left({z}\right)\:{and}\:{Im}\left({z}\right)\:{of}\:\left[\left({e}^{{i}\left(\mathrm{1}+\mathrm{2}{k}\right)\pi} \right)^{\frac{\mathrm{1}}{\mathrm{10}}} +\mathrm{1}\right]^{−\mathrm{1}} \\ $$$$ \\ $$ Commented by mohammad17 last updated on 21/Apr/21 $$???? \\…
Question Number 73488 by abdomathmax last updated on 13/Nov/19 $${solve}\:\:\:{xy}^{''} \:\:+\left({x}^{\mathrm{2}} −\mathrm{1}\right){y}^{'} \:\:={x}\:{e}^{−{x}^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated on 14/Nov/19…
Question Number 73489 by abdomathmax last updated on 13/Nov/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{3}+{x}^{\mathrm{2}} \right)}{\left(\mathrm{2}\:{x}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73486 by abdomathmax last updated on 13/Nov/19 $${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 $${P}\left({x}\right)=\mathrm{0}\:\Leftrightarrow\frac{\left(\mathrm{1}−{ix}\right)^{{n}} }{\left(\mathrm{1}+{ix}\right)^{{n}}…
Question Number 73487 by abdomathmax last updated on 13/Nov/19 $${let}\:\:\:\:\alpha\:{and}\:\beta\:{roots}\:{of}\:\:{the}\:{equation}\:\:{x}^{\mathrm{2}} −{x}+\mathrm{2}=\mathrm{0} \\ $$$${simplify}\:\:\:{A}_{{p}} =\:\alpha^{{p}} \:+\beta^{{p}} \:{and}\:{calculate} \\ $$$$\sum_{{p}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{A}_{{p}} \:\:{and}\:\sum_{{p}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:{A}_{{p}} ^{\mathrm{2}} \\…
Question Number 139023 by mohammad17 last updated on 21/Apr/21 $${find}\:{Re}\left({z}\right)\:{and}\:{Im}\left({z}\right)\:{of}\:{z}=\left(−\mathrm{2}{i}\right)^{−\frac{\mathrm{3}}{\mathrm{2}}} \\ $$ Answered by MJS_new last updated on 21/Apr/21 $$−\mathrm{2i}=\mathrm{2e}^{−\frac{\pi}{\mathrm{2}}\mathrm{i}} \\ $$$$\left(\mathrm{2e}^{−\frac{\pi}{\mathrm{2}}\mathrm{i}} \right)^{−\frac{\mathrm{3}}{\mathrm{2}}} =\mathrm{2}^{−\frac{\mathrm{3}}{\mathrm{2}}} \mathrm{e}^{\frac{\mathrm{3}\pi}{\mathrm{4}}\mathrm{i}}…
Question Number 73484 by abdomathmax last updated on 13/Nov/19 $${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{{n}} } \\ $$$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{F}\left({x}\right){dx} \\ $$ Answered by mind is power…
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:…