Question Number 74017 by mathmax by abdo last updated on 17/Nov/19 $${let}\:{f}\left({x}\right)=\int_{{x}} ^{{x}^{\mathrm{2}} +\mathrm{3}} \:{e}^{−{xt}} \:{ln}\left(\mathrm{1}+{e}^{−{xt}} \right){dt}\:\:\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\ $$ Commented…
Question Number 74013 by mathmax by abdo last updated on 17/Nov/19 $${let}\:\:\:{P}\left({x}\right)=\:\sum_{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} \:{x}^{{i}+{j}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{P}\:^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{P}\left({x}\right){dx} \\ $$ Commented by abdomathmax…
Question Number 74015 by mathmax by abdo last updated on 17/Nov/19 $${let}\:{f}\left({x}\right)\:=\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{sh}\left({xt}\right)}{{sin}\left({xt}\right)}{dt} \\ $$$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right) \\ $$ Commented by mathmax by abdo…
Question Number 73697 by mathmax by abdo last updated on 14/Nov/19 $${find}\:{a}\:{formulae}\:{for}\:{calculus}\:{of}\:{arctan}\left({x}+{iy}\right) \\ $$ Commented by mathmax by abdo last updated on 15/Nov/19 $${we}\:{have}\:{proved}\:{that}\:{arctanz}\:=\frac{\mathrm{1}}{\mathrm{2}{i}}{ln}\left(\frac{\mathrm{1}+{iz}}{\mathrm{1}−{iz}}\right)\:\Rightarrow \\…
Question Number 139032 by bramlexs22 last updated on 21/Apr/21 Answered by EDWIN88 last updated on 21/Apr/21 $$\:\ell\mathrm{et}\:\mathrm{y}=\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\:\Rightarrow\mathrm{xy}+\mathrm{y}=\mathrm{1}−\mathrm{x}\: \\ $$$$\:\mathrm{xy}+\mathrm{x}=\mathrm{1}−\mathrm{y}\:\Rightarrow\:\mathrm{x}=\frac{\mathrm{1}−\mathrm{y}}{\mathrm{1}+\mathrm{x}} \\ $$$$\:\left(\mathrm{f}\left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)\right)^{\mathrm{2}} .\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\:\ldots\left(\mathrm{1}\right) \\ $$$$\left(\mathrm{f}\left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)\right).\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} \:=\:\mathrm{x}\:\ldots\left(\mathrm{2}\right)…
Question Number 139029 by bramlexs22 last updated on 21/Apr/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)=\:\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$ Answered by EDWIN88 last updated on 21/Apr/21 $$\:\:\:\:\:\:\:\:\:\mathrm{u}=\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} } \\…
Question Number 73491 by abdomathmax last updated on 13/Nov/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:{e}^{−\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}} \:{dx} \\ $$ Commented by mathmax by abdo last updated on 14/Nov/19…
Question Number 73490 by abdomathmax last updated on 13/Nov/19 $${calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left({x}^{\mathrm{2}} \:+\frac{{a}}{{x}^{\mathrm{2}} }\right)} {dx}\:\:{with}\:{a}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73488 by abdomathmax last updated on 13/Nov/19 $${solve}\:\:\:{xy}^{''} \:\:+\left({x}^{\mathrm{2}} −\mathrm{1}\right){y}^{'} \:\:={x}\:{e}^{−{x}^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated on 14/Nov/19…
Question Number 73487 by abdomathmax last updated on 13/Nov/19 $${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}} \\…