Question Number 28530 by abdo imad last updated on 26/Jan/18 $${prove}\:{that}\:\mid{sinx}\mid=\:\frac{\mathrm{8}}{\pi}\:\sum_{{n}=\mathrm{1}} ^{+\infty} \:\frac{{sin}^{\mathrm{2}} \left({nx}\right)}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28531 by abdo imad last updated on 26/Jan/18 $${let}\:{give}\:\:{S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{k}^{{p}} \:\:\:\:,\:{p}\in{N}\:\:{and}\:{n}\geqslant\mathrm{1} \\ $$$${find}\:{the}\:{radius}\:{of}\:{convergence}\:{of}\:{the}\:{serie}\:\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{{x}^{{n}} }{{S}_{{n}} }\:. \\ $$ Terms of Service…
Question Number 28436 by abdo imad last updated on 25/Jan/18 $${study}\:{the}\:{nature}\:{of}\:{sequence}\:\left({u}_{{n}} \right)\:/\:{u}_{\mathrm{0}} =\mathrm{1}\:{and} \\ $$$${u}_{{n}+\mathrm{1}} =\:\:\frac{\mathrm{1}}{{u}_{{n}\:} +\:{e}^{−{n}} }\:. \\ $$ Terms of Service Privacy Policy…
Question Number 28428 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:{f}_{{n}} \left({x}\right)=\:\left(\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{{n}} \right)^{\left({n}\right)} \:\:\:{find}\:\:{f}_{{n}} \:. \\ $$ Commented by abdo imad last updated on…
Question Number 93908 by abdomathmax last updated on 16/May/20 $${calculste}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{arctan}\left({xt}\right)}{{t}+{x}}{dt} \\ $$ Commented by redmiiuser last updated on 16/May/20 $${Answer}:\mathrm{0} \\ $$…
Question Number 93899 by mathmax by abdo last updated on 16/May/20 $${find}\:{a}\:{function}\:{f}\:{continue}\:{on}\:\left[{a},{b}\right]\:{wich}\:{verify} \\ $$$$\left(\int_{{a}} ^{{b}} {f}\left({x}\right){dx}\right)^{\mathrm{2}} \:=\int_{{a}} ^{{b}} \:{f}^{\mathrm{2}} \left({x}\right){dx}\: \\ $$ Terms of Service…
Question Number 28169 by abdo imad last updated on 21/Jan/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{\left({lnx}\right)^{{k}} }{\mathrm{1}−{x}}{dx}=\left(−\mathrm{1}\right)^{{k}} \:\left({k}!\right)\xi\left({k}+\mathrm{1}\right)\:\:. \\ $$ Commented by abdo imad last updated on 23/Jan/18…
Question Number 28168 by abdo imad last updated on 21/Jan/18 $${find}\:{the}\:{nature}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} {arcos}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{{a}} }\right){z}^{{n}} \:\:{with}\:{a}>\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28138 by abdo imad last updated on 21/Jan/18 $${studie}\:{and}?{give}\:{the}\:{graph}\:{for}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\:{e}^{{x}} \:\:−{x}^{{e}} \:\:\:\:\:. \\ $$ Commented by abdo imad last updated on 26/Jan/18…
Question Number 93464 by i jagooll last updated on 13/May/20 $$\mathrm{If}\:\mathrm{f}\:\mathrm{a}\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{f}\left(\mathrm{a}\right).\mathrm{f}\left(\mathrm{b}\right)−\mathrm{f}\left(\mathrm{a}+\mathrm{b}\right)=\mathrm{a}+\mathrm{b}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{2019}\right)\: \\ $$ Answered by prakash jain last updated on 13/May/20…