Question Number 30478 by abdo imad last updated on 22/Feb/18 $${let}\:{give}\:\:{l}_{{i}} \left({x}\right)=\:\int_{\mathrm{2}} ^{{x}} \:\:\:\frac{{dt}}{{ln}\left({t}\right)}\:{find}\:{a}\:{serie}\:{equal}\:{to}\:{l}_{{i}} \left({x}\right). \\ $$$${x}\geqslant\mathrm{2}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 30477 by abdo imad last updated on 22/Feb/18 $${f}\:{function}\:\mathrm{2}\left(×\right)\:{derivable}\:{prove}\:{that} \\ $$$${L}\left({f}^{'} \right)=\:{pL}\left({f}\right)\:−{f}\left({o}\right)\:{and}\:{L}\left({f}^{''} \right)={p}^{\mathrm{2}} {L}\left({f}\right)−{pf}\left(\mathrm{0}\right)−{f}^{'} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{let}\:{f}\left({t}\right)={tsin}\left({wt}\right)\:{find}\:{L}\left({f}\right). \\ $$ Terms of Service Privacy…
Question Number 30475 by abdo imad last updated on 22/Feb/18 $${let}\:{give}\:{f}_{{n}} \left({x}\right)=\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\frac{{sin}\left({xt}\right)}{{t}}\:{e}^{−{t}} \:{dt} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow\infty} {f}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{another}\:{form}\:{of}\:{f}_{{n}} \left({x}\right)\:{by}\:{calculating}\:{f}_{{n}} ^{'} \left({x}\right). \\…
Question Number 30476 by abdo imad last updated on 22/Feb/18 $${find}\:{L}\left({cos}^{\mathrm{2}} {x}\right)\:{and}\:{L}\left({sin}^{\mathrm{2}} {x}\right)\:{L}\:{is}\:{laplace}\:{transform}. \\ $$ Answered by sma3l2996 last updated on 24/Feb/18 $${L}\left({cos}^{\mathrm{2}} {x}\right)={L}\left(\frac{{cos}\left(\mathrm{2}{x}\right)+\mathrm{1}}{\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left({L}\left({cos}\left(\mathrm{2}{x}\right)\right)+{L}\left(\mathrm{1}\right)\right) \\…
Question Number 161537 by cortano last updated on 19/Dec/21 $$\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{1}+\mathrm{tan}\:^{\mathrm{4}} \left({x}\right)}{\mathrm{cot}\:^{\mathrm{2}} \left({x}\right)}\:{dx}\:=? \\ $$ Answered by Ar Brandon last updated on 19/Dec/21 $$=\int_{\mathrm{0}}…
Question Number 30441 by abdo imad last updated on 22/Feb/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left[{x}\right]^{\mathrm{2}} } =\:\sum_{{n}\geqslant\mathrm{0}} \:{e}^{−{n}^{\mathrm{2}} } . \\ $$ Answered by alex041103 last updated…
Question Number 30442 by abdo imad last updated on 22/Feb/18 $${prove}\:{that}\:\:\:\frac{\mathrm{1}}{{e}}\:\leqslant\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−\left({x}−\left[{x}\right]\right)^{\mathrm{2}} } \:{dx}\leqslant\mathrm{1}. \\ $$ Commented by alex041103 last updated on 22/Feb/18 $${You}\:{can}\:{see}\:{that}\:{if}\:{x}\in\left[\mathrm{0},\mathrm{1}\right),\:{then}…
Question Number 30426 by abdo imad last updated on 22/Feb/18 $${find}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{integr}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30423 by abdo imad last updated on 22/Feb/18 $${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sint}}{{t}^{\alpha} }{dt}\:.\:\alpha{from}\:{R}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30413 by abdo imad last updated on 22/Feb/18 $${study}\:{the}\:{convergence}\:{of}\:\:{A}\left(\alpha\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left({t}\right)\:{arctant}}{{t}^{\alpha} }{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com