Category: Relation and Functions

Question Number 32934 by abdo imad last updated on 06/Apr/18 $$letgive\mid x\mid <1provethat$$$$\sum _{n=1}^{\mathrm{\infty }}{x}^{n}cos\left(n\theta \right)=\frac{xcos\theta -x^2}{1-2xcos\theta +x^2}$$ Terms of Service Privacy Policy…

Question Number 98430 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{let}\mathrm{g}\left(\mathrm{x}\right)=\frac{2}{\cos \left(\pi \mathrm{x}\right)}\mathrm{developp}\mathrm{g}\mathrm{at}\mathrm{fourier}\mathrm{serie}$$ Answered by abdomathmax last updated on 13/Jun/20 $$\mathrm{we}\:\mathrm{have}\:\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{2}}{\mathrm{cos}\left(\pi\mathrm{x}\right)}\:=\frac{\mathrm{4}}{\mathrm{e}^{\mathrm{i}\pi\mathrm{x}\:} \:+\mathrm{e}^{−\mathrm{i}\pi\mathrm{x}} } \…

Question Number 98424 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{calculste}{\mathrm{A}}_{\mathrm{n}}={\int }_{-\frac{1}{2}}^{\frac{1}{2}}{\mathrm{x}}^{\mathrm{n}}\sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}}\mathrm{dx}$$$$\mathrm{find}\mathrm{nature}\mathrm{of}\mathrm{the}\mathrm{serie}\mathrm{\Sigma }{\mathrm{A}}_{\mathrm{n}}$$ Answered by maths mind last…

Question Number 98310 by mathmax by abdo last updated on 12/Jun/20 $$\mathrm{prove}\mathrm{by}\mathrm{using}\mathrm{serie}\mathrm{that}{\int }_0^{\mathrm{\infty }}\cos \left({\mathrm{x}}^2\right)\mathrm{dx}={\int }_0^{\mathrm{\infty }}\sin \left({\mathrm{x}}^2\right)\mathrm{dx}$$ Terms of Service Privacy Policy…

Question Number 32734 by caravan msup abdo. last updated on 01/Apr/18 $$1)a⩾0calculate{\int }_0^a\frac{n^2-x^2}{{(n^2+x^2)}^2}dxwith$$$$nintegr$$$$\left.\mathrm{2}\right)\:{find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{n}^{\mathrm{2}}…