Question Number 33167 by abdo imad last updated on 11/Apr/18 $${f}\:{is}\:{a}\:{continue}\:{and}\:{positive}\:{function}\:{on}\:\left[{a},{b}\right]\:{with}\:{a}<{b} \\ $$$${let}\:{m}\:={max}_{{x}\in\left[{a},{b}\right]} \:{f}\left({x}\right)\:{prove}\:{that} \\ $$$${lim}_{{n}\rightarrow\infty} \:\:\left(\:\frac{\mathrm{1}}{{b}−{a}}\:\int_{{a}} ^{{b}} \:{f}^{{n}} \left({x}\right){dx}\right)^{\frac{\mathrm{1}}{{n}}} \\ $$ Commented by abdo…
Question Number 33131 by prof Abdo imad last updated on 11/Apr/18 $$\left.\mathrm{1}\right){find}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{e}^{{inx}} }{{n}\left({n}+\mathrm{1}\right)} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{{sin}\left({nx}\right)}{{n}\left({n}+\mathrm{1}\right)} \\ $$$${and}\:\sum_{{n}\geqslant\mathrm{1}} \:\:\frac{{cos}\left({nx}\right)}{{n}\left({n}+\mathrm{1}\right)}\:. \\ $$ Commented by…
Question Number 33127 by prof Abdo imad last updated on 10/Apr/18 $$\:{find}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({na}\right)}{\left({sina}\right)^{{n}} }\:\frac{{x}^{{n}} }{{n}!}\:\:{with}\:\mathrm{0}<{a}<\pi\:. \\ $$ Commented by prof Abdo imad last updated…
Question Number 33126 by prof Abdo imad last updated on 10/Apr/18 $${let}\:{give}\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} \:−\mathrm{3}{x}+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{if}\:\:\:\:{f}\left({x}\right)=\Sigma\:{a}_{{n}} \:{x}^{{n}} \:\:{calculate}\:{the}\:{sequence}\:{a}_{{n}} \\ $$…
Question Number 33124 by prof Abdo imad last updated on 10/Apr/18 $${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\mathrm{2}^{{n}−\mathrm{1}} }\:. \\ $$ Commented by prof Abdo imad last updated on…
Question Number 98657 by mathmax by abdo last updated on 15/Jun/20 $$\mathrm{solve}\:\:\mathrm{y}^{''} \:−\mathrm{3y}^{'} \:\:+\mathrm{2y}\:=\frac{\mathrm{sinx}}{\mathrm{x}} \\ $$ Answered by maths mind last updated on 15/Jun/20 $${y}''−\mathrm{3}{y}'+\mathrm{2}{y}=\mathrm{0}…
Question Number 98656 by mathmax by abdo last updated on 15/Jun/20 $$\mathrm{solve}\:\:\:\mathrm{xy}^{''} \:+\left(\mathrm{2}+\mathrm{x}^{\mathrm{2}} \right)\mathrm{y}^{'} \:\:=\mathrm{xe}^{−\mathrm{x}^{\mathrm{2}} } \\ $$ Answered by MWSuSon last updated on 15/Jun/20…
Question Number 164176 by mathlove last updated on 15/Jan/22 Answered by mr W last updated on 15/Jan/22 $${f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)={x}\:\:\:\:…\left({i}\right) \\ $$$${replace}\:{x}\:{with}\:\mathrm{1}−\frac{\mathrm{1}}{{x}} \\ $$$$\Rightarrow{f}\left(\frac{{x}−\mathrm{1}}{{x}}\right)+{f}\left({x}\right)=\mathrm{1}−\frac{\mathrm{1}}{{x}}\:\:\:…\left({ii}\right) \\ $$$${replace}\:{x}\:{with}\:\frac{\mathrm{1}}{\mathrm{1}−{x}} \\…
Question Number 33094 by abdo imad last updated on 10/Apr/18 $${let}\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\mathrm{1}+{x}+{x}^{\mathrm{2}} }\:\:{dvelopp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$ Commented by prof Abdo imad last updated on 11/Apr/18 $${f}\left({x}\right)\:{is}\:{developped}\:{at}\:{form}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty}…
Question Number 33074 by prof Abdo imad last updated on 10/Apr/18 $${find}\:{interms}\:{of}\:{n}\:\:{the}\:{sum}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:\:{C}_{{n}} ^{{k}} \\ $$ Commented by abdo imad last updated on…