Question Number 91683 by M±th+et+s last updated on 02/May/20 Commented by M±th+et+s last updated on 02/May/20 $${what}\:{is}\:{the}\:{difference}\:{between}\:{them}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 157209 by aliyn last updated on 21/Oct/21 Commented by aliyn last updated on 21/Oct/21 $${prove}\:{this}\:?? \\ $$ Commented by cortano last updated on…
Question Number 91667 by Ar Brandon last updated on 02/May/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{of}\: \\ $$$$\mathrm{1}.\:\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{k}^{\mathrm{2}} }\:\:\: \\ $$$$\mathrm{2}.\:\mathrm{v}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{2kn}}} \\…
Question Number 157198 by Fresnel last updated on 20/Oct/21 $$\mathrm{M}{ontrer}\:{que}\:{l}'{ensemble}\:{Q}\:{n}'{est}\:{ni}\:{ferme}\:{ni}\:{ouvert} \\ $$ Answered by TheHoneyCat last updated on 21/Oct/21 $$ \\ $$$$\frac{\sqrt{\mathrm{2}}}{\mathrm{2}^{{n}} }\underset{{n}\rightarrow\infty} {\rightarrow}\mathrm{0}\in\mathbb{Q} \\…
Question Number 157191 by naka3546 last updated on 20/Oct/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{sin}\:{x}\:−\:{x}\:+\:\frac{\mathrm{1}}{\mathrm{6}}\:{x}^{\mathrm{3}} }{{x}^{\mathrm{5}} }\:\:\:=\:\:? \\ $$$$\left(\:{Without}\:\:{L}'{Hospital}\:,\:{Taylor}\:\:{or}\:\:{Maclaurin}\:\:{Series}\:\right)\:. \\ $$ Answered by puissant last updated on 20/Oct/21 $${We}\:{have}\:{x}−\frac{{x}^{\mathrm{3}}…
Question Number 157177 by mathocean1 last updated on 20/Oct/21 Answered by puissant last updated on 20/Oct/21 Commented by mathocean1 last updated on 22/Oct/21 $${thanks}\:{le}\:{puissant}. \\…
Question Number 157168 by mathocean1 last updated on 20/Oct/21 $${x}\:,\:{y}\:{and}\:{z}\:{are}\:{numbers}. \\ $$$${Show}\:{that}\:{max}\left({x},\:{y}\right)=\frac{{x}+{y}+\mid{x}−{y}\mid}{\mathrm{2}}\:{and}\:{min}\left({x},{y}\right)=\frac{{x}+{y}−\mid{x}−{y}\mid}{\mathrm{2}} \\ $$$${then}\:{find}\:{a}\:{formula}\:{for}\: \\ $$$${max}\left({x},{y},{z}\right). \\ $$ Answered by puissant last updated on 20/Oct/21…
Question Number 157171 by mathocean1 last updated on 20/Oct/21 $${calculate}\:\underset{{n}\rightarrow+\infty} {{lim}}\left(\frac{{n}+{ln}\left({n}\right)+\mathrm{1}}{\left(\mathrm{5}+\sqrt{{n}}\right)^{\mathrm{2}} }\right) \\ $$ Answered by puissant last updated on 20/Oct/21 $$\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{n}+{ln}\left({n}\right)+\mathrm{1}}{\left(\mathrm{5}+\sqrt{{n}}\right)^{\mathrm{2}} }\right)=\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{n}\left(\mathrm{1}+\frac{{ln}\left({n}\right)}{{n}}+\frac{\mathrm{1}}{{n}}\right)}{{n}\left(\frac{\mathrm{5}}{\:\sqrt{{n}}}+\mathrm{1}\right)^{\mathrm{2}}…
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Question Number 91622 by Ar Brandon last updated on 02/May/20 $$\frac{\mathrm{d}\left(\mathrm{x}!\right)}{\mathrm{dx}}= \\ $$ Commented by MJS last updated on 02/May/20 $$\mathrm{we}\:\mathrm{had}\:\mathrm{this}\:\mathrm{several}\:\mathrm{times}\:\mathrm{before} \\ $$$${x}!\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no}\:\mathrm{derivate}\:\mathrm{exists} \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{mean}\:\Gamma\left({x}\right)\:\mathrm{you}\:\mathrm{must}\:\mathrm{say}\:\mathrm{it}……