Question Number 67380 by mathmax by abdo last updated on 26/Aug/19 $${solve}\:{the}\:\left({d}.{e}.\right)\:\:\:\:\left(\:{x}^{\mathrm{2}} −{x}+\mathrm{1}\:\:\:\:\:\:\right){y}^{'} −\left(\mathrm{2}{x}+\mathrm{3}\right){y}\:={x}^{\mathrm{2}} \:{e}^{{x}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 67381 by mathmax by abdo last updated on 26/Aug/19 $${let}\:{f}\left({x}\right)\:={x}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{2}\pi\:{periodic}\:\:{even}\:\:{develop}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Commented by mathmax by abdo last updated on 27/Aug/19 $${f}\:{even}\:\Rightarrow{f}\left({x}\right)\:=\frac{{a}_{\mathrm{0}}…
Question Number 1844 by 123456 last updated on 12/Oct/15 $$\mathrm{lets}\:\mathrm{two}\:\mathrm{polynimies}\:{p}_{{n}} ,{q}_{{n}} \:\mathrm{givwn}\:\mathrm{by} \\ $$$${p}_{\mathrm{1}} ={q}_{\mathrm{1}} ={x} \\ $$$${p}_{{n}+\mathrm{1}} ={p}_{{n}} +{q}_{{n}} \\ $$$${q}_{{n}+\mathrm{1}} ={p}_{{n}} {q}_{{n}} \\…
Question Number 67378 by mathmax by abdo last updated on 26/Aug/19 $${let}\:{f}\left({x}\right)\:={x}^{\mathrm{3}} \:\:\:\:\:\:,\mathrm{2}\pi\:{periodic}\:{odd} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\: \\ $$ Commented by mathmax by abdo last updated on…
Question Number 132912 by SEKRET last updated on 17/Feb/21 $$ \\ $$ Commented by mr W last updated on 17/Feb/21 $${a}\:{lot}\:{of}\:{your}\:{posts}\:{are}\:{just}\:{blank}. \\ $$$${accidentally}\:{or}\:{purposely}? \\ $$…
Question Number 67379 by mathmax by abdo last updated on 26/Aug/19 $${let}\:\:{f}\left({x}\right)\:={e}^{−\mid{x}\mid} \:\:\:\:\:\:\mathrm{2}\pi\:\:{periodic}\:{even} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Commented by Abdo msup. last updated on 28/Aug/19…
Question Number 1842 by 123456 last updated on 12/Oct/15 $${f}\left({x},{y}\right)={f}\left({x}+{y},{xy}\right) \\ $$$${f}\left({x},{y}\right)={x},−\mathrm{2}\leqslant{y}\leqslant\mathrm{2} \\ $$$${f}\left({x},{y}\right)={y},\mid{x}\mid\geqslant\mathrm{100}\vee\mid{y}\mid\geqslant\mathrm{100} \\ $$$${f}\left(\mathrm{0},\mathrm{0}\right)=? \\ $$$${f}\left(\mathrm{1},\mathrm{4}\right)=? \\ $$ Commented by 123456 last updated…
Question Number 67374 by mathmax by abdo last updated on 26/Aug/19 $${find}\:\int\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctan}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right){dx} \\ $$ Commented by Abdo msup. last updated on 27/Aug/19 $${let}\:{I}\:=\int\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arcran}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right){dx}\:{by}\:{psrts}…
Question Number 1839 by RasheedAhmad last updated on 11/Oct/15 $${Sum}\:{to}\:{n}\:{terms}\:{the}\:{series}: \\ $$$$\mathrm{0}\centerdot\mathrm{3}+\mathrm{0}\centerdot\mathrm{33}+\mathrm{0}\centerdot\mathrm{333}+… \\ $$$$ \\ $$ Answered by 112358 last updated on 12/Oct/15 $${We}\:{may}\:{begin}\:{by}\:{searching}\:{for} \\…
Question Number 1838 by 112358 last updated on 11/Oct/15 $${Show}\:{that} \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{1}}{{sinz}}=\frac{\mathrm{1}}{{z}}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left(\frac{\mathrm{1}}{{z}+{n}\pi}+\frac{\mathrm{1}}{{z}−{n}\pi}\right) \\ $$$$\left(\mathrm{2}\right)\:{cotz}=\frac{\mathrm{1}}{{z}}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{z}+{n}\pi}+\frac{\mathrm{1}}{{z}−{n}\pi}\right) \\ $$$${where}\:{z}\neq{m}\pi,\:{m}\in\mathbb{Z}\:,\:{given}\:{the}\:{fact}\:{that} \\ $$$${cosax}=\frac{\mathrm{2}{sina}\pi}{\pi}\left[\frac{\mathrm{1}}{\mathrm{2}{a}}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}}…