Category: Relation and Functions

Question Number 146902 by mathmax by abdo last updated on 16/Jul/21 $$\mathrm{let}\alpha \mathrm{and}\beta \mathrm{roots}\mathrm{of}{\mathrm{z}}^2+3\mathrm{z}+5=0$$$$\mathrm{simlify}{\mathrm{U}}_{\mathrm{n}}=\sum _{\mathrm{k}=0}^{\mathrm{n}}({\alpha }^{\mathrm{k}}+{\beta }^{\mathrm{k}})$$$$\mathrm{and}\:\mathrm{V}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\left(\frac{\mathrm{1}}{\alpha^{\mathrm{k}}…

Question Number 146898 by mathmax by abdo last updated on 16/Jul/21 $$\mathrm{calculate}{\int }_0^{\mathrm{\infty }}\frac{\mathrm{cosx}}{({\mathrm{x}}^2+1)({\mathrm{x}}^2+2)({\mathrm{x}}^2+3)}\mathrm{dx}$$ Answered by qaz last updated on…

Question Number 146705 by mathmax by abdo last updated on 15/Jul/21 $$\mathrm{find}{\lim }_{\mathrm{x}\to 0}\frac{\sin (\tan \left(2\mathrm{x}\right)-\mathrm{x})+1-\cos \left(\pi {\mathrm{x}}^2\right)}{{\mathrm{x}}^2}$$ Answered by Olaf_Thorendsen last updated on 15/Jul/21 $${f}\left({x}\right)\:=\:\frac{\mathrm{sin}\left(\mathrm{tan}\left(\mathrm{2}{x}\right)−{x}\right)+\mathrm{1}−\mathrm{cos}\left(\pi{x}\right)}{{x}^{\mathrm{2}}…

Question Number 146549 by mathmax by abdo last updated on 13/Jul/21 $$\mathrm{find}{\lim }_{\mathrm{x}\to 0}\frac{\cos (\mathrm{x}-\mathrm{sinx})+1-\cos \left({\mathrm{x}}^2\right)}{{\mathrm{x}}^2}$$ Answered by Olaf_Thorendsen last updated on 14/Jul/21 $$\frac{\mathrm{cos}\left({x}−\mathrm{sin}{x}\right)+\mathrm{1}−\mathrm{cos}\left({x}^{\mathrm{2}}…

Question Number 146548 by mathmax by abdo last updated on 13/Jul/21 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\cos \left(\alpha \mathrm{x}\right)\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{fourier}\mathrm{serie}\left(\alpha \mathrm{real}\right)$$ Answered by Olaf_Thorendsen last updated on 14/Jul/21 $${a}_{\mathrm{0}} \:=\:\frac{\mathrm{1}}{\mathrm{T}}\int_{−\frac{\mathrm{T}}{\mathrm{2}}} ^{+\frac{\mathrm{T}}{\mathrm{2}}} {f}\left({x}\right){dx}…