Category: Relation and Functions

Question Number 96196 by mathmax by abdo last updated on 30/May/20 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{sinx}\right)\:\:\mathrm{developp}\:\mathrm{g}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 31/May/20 $$\mathrm{g}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{sinx}\right)\:=\mathrm{ln}\left(\frac{\mathrm{e}^{\mathrm{ix}} −\mathrm{e}^{−\mathrm{ix}}…

Question Number 30601 by abdo imad last updated on 23/Feb/18 $${for}\:\mathrm{0}<{r}\leqslant\mathrm{1}\:{and}\:\left(\theta,{x}\right)\in{R}^{\mathrm{2}} \:\:{find} \\ $$$${S}=\sum_{{n}=\mathrm{0}} ^{\infty} \:{r}^{{n}} {cos}\left({n}\theta\right). \\ $$ Commented by abdo imad last updated…

Question Number 30563 by abdo imad last updated on 23/Feb/18 $${let}\:{f}\left({x}\right)=\mid{x}−\mathrm{2}\:\left[\frac{{x}+\mathrm{1}}{\mathrm{2}}\right]\mid \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}\:{is}\:{periodic} \\ $$$$\left.\mathrm{2}\right)\:{simplify}\:{f}\left({x}\right)\:{if}\:{p}\leqslant{x}+\mathrm{1}\:{and}\:{p}\in{Z}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 30556 by abdo imad last updated on 23/Feb/18 $${let}\:\:{S}_{{n}} \left({x}\right)=\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\:\frac{{sin}\left({kx}\right)}{{k}^{\mathrm{2}} \left({k}+\mathrm{1}\right)}\:\:{find}\:{lim}_{{n}\rightarrow\infty} {S}_{{n}} \left({x}\right). \\ $$ Terms of Service Privacy Policy Contact:…

Question Number 30552 by abdo imad last updated on 23/Feb/18 $${find}\:{s}\left({x}\right)=\:\sum_{{n}\geqslant\mathrm{0}} \:\frac{{sin}\left({na}\right)}{\left({sina}\right)^{{n}} }\:\frac{{x}^{{n}} }{{n}!}\:{and}\: \\ $$$${T}\left({x}\right)\:=\sum_{{n}\geqslant\mathrm{0}} \:\:\frac{{cos}\left({na}\right)}{\left({sina}\right)^{{n}} }\:\frac{{x}^{{n}} }{{n}!}\:. \\ $$ Terms of Service Privacy…