Question Number 37894 by abdo mathsup 649 cc last updated on 19/Jun/18 $${find}\:{nature}\:{of}\:{the}\:{serie} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{{C}_{{n}} ^{{k}} }\right){x}^{{n}} \\ $$ Terms of…
Question Number 37891 by abdo mathsup 649 cc last updated on 19/Jun/18 $${calculate}\:{B}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\left(−\mathrm{1}\right)^{{k}} \left(\mathrm{2}{k}^{\mathrm{2}} \:+\mathrm{1}\right)\:{interms}\:{of}\:{n}. \\ $$ Commented by prof Abdo imad…
Question Number 37892 by abdo mathsup 649 cc last updated on 19/Jun/18 $${let}\:\:\:{f}\left({x}\right)=\sqrt{{x}+\sqrt{{x}+\mathrm{1}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:\:{give}\:{the}\:{equation}\:{of}\:{assymtote}\:{at}\:{point} \\ $$$${A}\left(\mathrm{0},{f}\left({o}\right)\right) \\ $$$$\left.\mathrm{3}\right)\:{if}\:{f}\left({x}\right)\sim\:{a}\left({x}−\mathrm{1}\right)\:\:+{b}\:\:\left({x}\rightarrow\mathrm{1}\right)\:{determine}\:{a}\:{andb} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\…
Question Number 103412 by abdomsup last updated on 14/Jul/20 $${solve}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} {y}^{''} \:+\mathrm{2}{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} \:+\mathrm{2}=\mathrm{0} \\ $$ Answered by OlafThorendsen last updated on 15/Jul/20 $$\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 103411 by abdomsup last updated on 14/Jul/20 $${solve}\:{x}^{\mathrm{2}} {y}^{''} \:+{xy}^{'} \:+{y}\:=\mathrm{0} \\ $$ Answered by bemath last updated on 14/Jul/20 $${set}\:{y}={x}^{{r}} \\ $$$${y}'={rx}^{{r}−\mathrm{1}}…
Question Number 37818 by prof Abdo imad last updated on 17/Jun/18 $${let}\:\mathrm{0}<{u}_{\mathrm{0}} <\mathrm{1}\:\:{and}\:{u}_{{n}+\mathrm{1}} =\sqrt{\frac{\mathrm{1}+{u}_{{n}} }{\mathrm{2}}} \\ $$$${study}\:{the}\:{convergence}\:{of}\:{u}_{{n}} \: \\ $$$$ \\ $$ Commented by math…
Question Number 37819 by prof Abdo imad last updated on 17/Jun/18 $${study}\:{the}\:{convergence}\:\:{of} \\ $$$${u}_{{n}+\mathrm{1}} ={u}_{{n}} \:+\:{ln}\left(\mathrm{1}+{e}^{−{u}_{{n}} } \right)\:\:{with}\:{u}_{\mathrm{0}} =\mathrm{0} \\ $$ Terms of Service Privacy…
Question Number 37817 by prof Abdo imad last updated on 17/Jun/18 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \:{x}^{{n}} \left(\mathrm{1}−{cos}\left(\frac{\pi}{{x}^{{n}} }\right)\right)\:{with}\:{x} \\ $$$${from}\:{R}\:{and}\:{x}\neq\mathrm{0} \\ $$ Commented by prof Abdo imad last…
Question Number 168800 by MikeH last updated on 17/Apr/22 $$\mathrm{If}\:\mathrm{the}\:\mathrm{function}\:{f}\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{in}\:\left[{a},{b}\right] \\ $$$$\mathrm{express}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left(\frac{{k}}{{n}}\right)\:\mathrm{as}\:\mathrm{a}\:\mathrm{definite} \\ $$$$\mathrm{integral}. \\ $$ Commented by safojontoshtemirov last updated on…
Question Number 37355 by math khazana by abdo last updated on 12/Jun/18 $$\:{let}\:\Sigma\:{a}_{{n}} {x}^{{n}} \:\:\:{with}\:{radius}\:{of}\:{convergence}\:{R} \\ $$$${prove}\:{that}\:{R}\:=\:\frac{\mathrm{1}}{{lim}_{{n}\rightarrow+\infty} \:{sup}^{{n}} \sqrt{\mid{a}_{{n}} \mid}}\:\:. \\ $$ Terms of Service…