Question Number 33571 by Joel578 last updated on 19/Apr/18 $${f}\left({x}\right)\:=\:{x}^{\mathrm{20}} \:+\:{a}_{\mathrm{1}} {x}^{\mathrm{19}} \:+\:{a}_{\mathrm{2}} {x}^{\mathrm{18}} \:+\:…\:+\:{a}_{\mathrm{20}} \\ $$$$\mathrm{If}\:{f}\left(\mathrm{1}\right)\:=\:{f}\left(\mathrm{2}\right)\:=\:{f}\left(\mathrm{3}\right)\:=\:…\:=\:{f}\left(\mathrm{20}\right) \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}_{\mathrm{1}} \:? \\ $$ Answered by MJS…
Question Number 98945 by mathmax by abdo last updated on 17/Jun/20 $$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\:\int_{\mathrm{0}} ^{\mathrm{n}} \left(\mathrm{1}−\frac{\mathrm{t}}{\mathrm{n}}\right)^{\mathrm{n}} \mathrm{arctan}\left(\mathrm{nt}\right)\mathrm{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 98943 by mathmax by abdo last updated on 17/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$ Answered by maths mind last updated on 17/Jun/20 $${f}\left({x}\right)=\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 98940 by mathmax by abdo last updated on 17/Jun/20 $$\mathrm{if}\:\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} }\:=\sum_{\mathrm{m}=\mathrm{0}} ^{\infty} \:\mathrm{a}_{\mathrm{m}} \mathrm{x}^{\mathrm{m}} \:\:\:\:\mathrm{determinate}\:\mathrm{a}_{\mathrm{m}} \\ $$ Commented by mr W last updated…
Question Number 33375 by rahul 19 last updated on 15/Apr/18 $${If}\:{f}:{R}\:\rightarrow\:{R}\:{is}\:{an}\:\boldsymbol{{odd}}\:{function}\:{such} \\ $$$${that}\:: \\ $$$$\left.{a}\right)\:{f}\left(\mathrm{1}+{x}\right)\:=\:\mathrm{1}+{f}\left({x}\right)\:. \\ $$$$\left.{b}\right)\:{x}^{\mathrm{2}} \:{f}\left(\frac{\mathrm{1}}{{x}}\right)\:=\:{f}\left({x}\right)\:,\:{x}\neq\mathrm{0}. \\ $$$${Then}\:{find}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:? \\ $$ Commented by prof…
Question Number 33359 by caravan msup abdo. last updated on 15/Apr/18 $${let}\:{consider}\:{the}\:{serie}\:\sum_{{n}\geqslant\mathrm{1}} {sin}\left(\frac{\mathrm{1}}{\:\sqrt{{n}}}\right){x}^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{radius}\:{of}\:{convergence} \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{convergence}\:{at}\:−{R}\:{and}\:{R} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{S}\left({x}\right){its}\:{sum}\:{study}\:{the}\:{continuity} \\ $$$${of}\:{S} \\ $$$$\left.\mathrm{4}\right)\:{prove}\:{that}\:\left(\mathrm{1}−{x}\right)_{{x}\rightarrow\mathrm{1}^{−} } {S}\left({x}\right)\rightarrow\mathrm{0}…
Question Number 33358 by caravan msup abdo. last updated on 15/Apr/18 $${prove}\:{that}\:\sum_{{p}=\mathrm{1}} ^{\infty} \:\frac{{z}^{{p}} }{\mathrm{1}+{z}^{{p}} }\:=\sum_{{q}=\mathrm{1}} ^{\infty} \:\left(−\mathrm{1}\right)^{{q}−\mathrm{1}} \frac{{z}^{{q}} }{\mathrm{1}−{z}^{{q}} } \\ $$ Terms of…
Question Number 33354 by caravan msup abdo. last updated on 15/Apr/18 $${find}\:{the}\:{radius}\:{of}\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{{ln}\left({n}\right)}{\:\sqrt{{n}^{\mathrm{3}} \:+{n}+\mathrm{1}}}\:{z}^{{n}} \\ $$ Commented by math khazana by abdo last updated on…
Question Number 33355 by caravan msup abdo. last updated on 15/Apr/18 $${let}\:{a}\geqslant\mathrm{1}\:{find}\:{the}\:{radius}\:{of} \\ $$$$\sum_{{n}\geqslant\mathrm{1}} {arc}\:{cos}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{{a}} }\right){z}^{{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33348 by caravan msup abdo. last updated on 14/Apr/18 $${let}\:{S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{{k}}\:{and} \\ $$$$\underset{{n}} {{T}}\:=\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{\mathrm{2}{k}−\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}\:{S}_{{n}} \:\:{and}\:{lim}\:{T}_{{n}}…