Question Number 35619 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:{f}\left({x}\right)\:=\:{x}\mid{x}\mid\:\:{odd}\:\mathrm{2}\pi\:{periodic} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 35620 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:\:{f}\left({x}\right)\:={e}^{−{x}} \:{sinx}\:\:\:{odd}\:\mathrm{2}\pi\:{periodic}\: \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$ Commented by abdo mathsup 649 cc last…
Question Number 35617 by abdo mathsup 649 cc last updated on 21/May/18 $${integrate}\:{the}\:{e}.{d}\:.\:\:{y}^{''} \:\:+\left({x}−\mathrm{1}\right){y}\:=\:{e}^{−{x}} \:{sinx} \\ $$$${with}\:{y}\left(\mathrm{0}\right)\:=\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 35616 by abdo mathsup 649 cc last updated on 21/May/18 $${integrate}\:{the}\:{d}.{e}\:\:{y}^{''} \:−\mathrm{2}{y}^{'} \:+{y}\:=\:{x}^{\mathrm{2}} {ch}\left({x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 166684 by cortano1 last updated on 25/Feb/22 $$\:\:\:\:\:\:\mathrm{T}\:=\:\int\:\frac{\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)}{\mathrm{2x}+\mathrm{4}}\:\mathrm{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 35615 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:\:{S}_{{n}} \:=\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}} \\ $$$${calculate}\:{S}_{{n}} \:\:\:{interms}\:{of}\:{H}_{{n}} \:\:\:{with}\:{H}_{{n}} \:=\sum_{{k}=\mathrm{1}} ^{{n}} \frac{\mathrm{1}}{{k}} \\ $$…
Question Number 35613 by abdo mathsup 649 cc last updated on 21/May/18 $${find}\:\:{I}_{{a},{b}} =\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\frac{{e}^{{x}} }{\left(\mathrm{1}+{a}\:{e}^{{x}} \right)\left(\mathrm{1}+{be}^{{x}} \right)}{dx}\:.. \\ $$ Terms of Service Privacy…
Question Number 35611 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:{h}\left({t}\right)\:=\:{e}^{{t}−{e}^{{t}} } \:\:\:\:{and}\:{for}\:{n}\geqslant\mathrm{0}\:{we}\:{put} \\ $$$${h}_{{n}} \left({t}\right)\:={nh}\left({nt}\right) \\ $$$${calculate}\:\:\int_{−\infty} ^{+\infty} \:{h}_{{n}} \left({t}\right){dt}\:. \\ $$…
Question Number 35612 by abdo mathsup 649 cc last updated on 21/May/18 $${calculate}\:{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\left(\mathrm{1}+{t}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} \:\:\:−\left(\mathrm{1}+{t}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} }{{t}}{dt}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 35610 by abdo mathsup 649 cc last updated on 21/May/18 $$\left.{let}\:{give}\:{x}\in\right]\mathrm{0},\mathrm{2}\pi\left[\:\:{and}\:{a}\:\in{R},{b}\in\:{R}\right. \\ $$$${prove}\:{that}\:\:\frac{\pi−{x}}{\mathrm{2}}\:=\:{arctan}\left(\frac{{sinx}}{\mathrm{1}−{cosx}}\right) \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\mid{arctan}\left({a}\right)−{arctan}\left({b}\right)\mid\leqslant\mid{a}−{b}\mid \\ $$$$\left.\mathrm{3}\left.\right){let}\theta\:\in\right]\mathrm{0},\frac{\pi}{\mathrm{2}}\left[\:\:,\:{x}\:\in\left[\theta,\mathrm{2}\pi−\theta\right]\:,\:{r}\in\left[\mathrm{0},\mathrm{1}\left[\:{prove}\:{that}\right.\right.\right. \\ $$$$\mid\varphi\left({x},{r}\right)\:−\frac{\pi−{x}}{\mathrm{2}}\mid\leqslant\:\:\frac{\mathrm{1}−{r}}{\left(\mathrm{1}−{cos}\theta\right)^{\mathrm{2}} } \\ $$ Terms…