Question Number 66875 by Cmr 237 last updated on 20/Aug/19 Commented by mathmax by abdo last updated on 20/Aug/19 $${convergence}\:{of}\:{this}\:{serie}\:\:\:{let}\:\varphi\left({t}\right)\:=\frac{\mathrm{1}}{{t}^{\mathrm{3}} {sin}^{\mathrm{2}} {t}}\:\:{with}\:{t}>\mathrm{1} \\ $$$${we}\:{have}\:\varphi^{'} \left({t}\right)\:=\:−\frac{\mathrm{3}{t}^{\mathrm{2}}…
Question Number 1055 by 123456 last updated on 24/May/15 $$\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$${g}:\left[\mathrm{0},\mathrm{1}\right]×\mathbb{N}\rightarrow\mathbb{R} \\ $$$${g}_{{n}} \left({x}\right)={f}\left[{g}_{{n}−\mathrm{1}} \left({x}\right)\right] \\ $$$${g}_{\mathrm{0}} \left({x}\right)={x} \\ $$$$\mathscr{A}\left\{{f}\right\}\left({n}\right)=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{f}\left({t}\right){g}_{{n}} \left({t}\right){dt} \\…
Question Number 1034 by 123456 last updated on 21/May/15 $${x}={i}+{f},{i}\in\mathbb{N},{f}\in\left[\mathrm{0},\mathrm{1}\right) \\ $$$${x}^{\mathrm{2}} =\left({i}+{f}\right)^{\mathrm{2}} ={i}^{\mathrm{2}} +\mathrm{2}{if}+{f}^{\mathrm{2}} \\ $$$${x}\in\mathbb{R}_{+} \\ $$$${i}+\mathrm{2}{f}=\mathrm{2}\Rightarrow{x}^{\mathrm{2}} =\mathrm{2}{i}+{f}^{\mathrm{2}} \\ $$$$\mathrm{2}{if}=\mathrm{0}\Rightarrow{x}^{\mathrm{2}} ={i}^{\mathrm{2}} +{f}^{\mathrm{2}} \\…
Question Number 66418 by 888 last updated on 14/Aug/19 $${what}\:{operation}\:{on}\:{interger}\:{used}\:{in}\:\mathrm{9}\left(\mathrm{7}.\mathrm{8}\right)=\left(\mathrm{9}.\mathrm{7}\right).\mathrm{8}?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 746 by 123456 last updated on 06/Mar/15 $${lets}\:\boxplus:\left(\mathbb{R}^{+} \right)^{\mathrm{2}} \rightarrow\mathbb{R}^{+} \\ $$$${defined}\:{by}\:{x}\boxplus{y}=\sqrt{\lfloor{x}\rfloor\lceil{x}\rceil}+{y} \\ $$$$\mathrm{1}.\:{x}\boxplus{y}\overset{?} {=}{y}\boxplus{x} \\ $$$$\mathrm{2}.{x}\boxplus\left({y}\boxplus{z}\right)\overset{?} {=}\left({x}\boxplus{y}\right)\boxplus{z} \\ $$$$\mathrm{3}.\exists{e},\forall{x}\in\mathbb{R}^{+} ,{x}\boxplus{e}={x}\:? \\ $$$$\mathrm{4}.\exists{e},\forall{x}\in\mathbb{R}^{+}…