Category: Relation and Functions

Question Number 31417 by abdo imad last updated on 08/Mar/18 $$letgive{u}_n=\sum _{k=1}^n\frac{1}{k}-ln\left(n\right)$$$$1)provethat{u}_{n}isconvergent$$$$2)if\gamma ={lim}_{n\to \mathrm{\infty }}{u}_{n}provethe0<\gamma <1.$$ Terms of…

Question Number 96836 by mathmax by abdo last updated on 05/Jun/20 $${\mathrm{a}}_{\mathrm{n}}\mathrm{is}\mathrm{a}\mathrm{sequence}\mathrm{wich}\mathrm{verify}{\mathrm{a}}_{\mathrm{n}+1}+{\mathrm{a}}_{\mathrm{n}}=\frac{1}{\mathrm{n}+1}\mathrm{\forall }\mathrm{n}$$$$\mathrm{calculate}\sum _{\mathrm{n}=0}^{\mathrm{\infty }}{\mathrm{a}}_{\mathrm{n}}{\mathrm{x}}^{\mathrm{n}}$$ Answered by Smail…

Question Number 96826 by bobhans last updated on 05/Jun/20 $$\mathrm{If}2\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}(\mathrm{x}-1)={\mathrm{x}}^2.\mathrm{determine}\mathrm{f}\left(\mathrm{x}\right)$$ Answered by john santu last updated on 05/Jun/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)={px}^2+qx+r$$$$\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\:{px}^{\mathrm{2}}…

Question Number 96773 by abdomathmax last updated on 04/Jun/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{″}}-\mathrm{y}=\frac{\mathrm{sinx}}{\mathrm{x}}$$ Answered by abdomathmax last updated on 05/Jun/20 $$\mathrm{let}\mathrm{solve}\mathrm{by}\mathrm{laplace}$$$$\left(\mathrm{e}\right)\Rightarrow\mathrm{L}\left(\mathrm{y}^{''} \right)−\mathrm{L}\left(\mathrm{y}\right)\:=\mathrm{L}\left(\frac{\mathrm{sinx}}{\mathrm{x}}\right)\:\Rightarrow \…

Question Number 96659 by mathmax by abdo last updated on 03/Jun/20 $$\mathrm{find}\mathrm{L}\left(\frac{\mathrm{sh}\left(3\mathrm{x}\right)}{\mathrm{x}}\right)\mathrm{L}\mathrm{laplace}\mathrm{transform}$$ Answered by Sourav mridha last updated on 07/Jun/20 $$\boldsymbol{{f}}\left(\boldsymbol{{a}}\right)=\int_{\mathrm{0}} ^{\infty} \boldsymbol{{e}}^{−\boldsymbol{{ax}}}…