Question Number 176652 by floor(10²Eta[1]) last updated on 24/Sep/22 $$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\begin{cases}{\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{r}^{\mathrm{2}} −\mathrm{1}}} \:\mathrm{if}\:\mathrm{r}<\mathrm{1},\:\mathrm{where}\:\mathrm{r}=\parallel\left(\mathrm{x},\mathrm{y}\right)\parallel}\\{\mathrm{0}\:\mathrm{if}\:\mathrm{r}\geqslant\mathrm{1}}\end{cases} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{in}\:\mathbb{R}^{\mathrm{2}} \\ $$ Answered by floor(10²Eta[1]) last updated on 24/Sep/22 $$\mathrm{recall}\:\mathrm{that}\:\parallel\left(\mathrm{x},\mathrm{y}\right)\parallel=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}}…
Question Number 176648 by mokys last updated on 23/Sep/22 $$\int\:\frac{{dx}}{{a}+{bcosx}}\:\:\:\: \\ $$$$ \\ $$$$\int\:\frac{{dx}}{{a}−{bsinx}} \\ $$ Commented by mokys last updated on 24/Sep/22 $$\left.?\left.?\left.?\left.\right]\right]\right]\right] \\…
Question Number 111067 by Algoritm last updated on 01/Sep/20 Commented by Her_Majesty last updated on 01/Sep/20 $${I}\:{don}'{t}\:{think}\:{so} \\ $$$${lim}_{{k}\rightarrow\infty} \frac{\underset{{j}=\mathrm{1}} {\overset{{k}} {\sum}}{j}^{\mathrm{7}} }{{k}!}={lim}_{{k}\rightarrow\infty} \frac{\frac{{k}^{\mathrm{8}} }{\mathrm{8}}+\frac{{k}^{\mathrm{7}}…
Question Number 45527 by Sanjarbek last updated on 14/Oct/18 Commented by Meritguide1234 last updated on 14/Oct/18 Commented by maxmathsup by imad last updated on 14/Oct/18…
Question Number 176595 by MASANJAJJ last updated on 22/Sep/22 Answered by Rasheed.Sindhi last updated on 22/Sep/22 $$\left.\mathrm{b}\right) \\ $$$$\:\:\:\left(\mathrm{2}{k}\right)^{\mathrm{2}} +\left(\mathrm{2}{k}+\mathrm{2}\right)^{\mathrm{2}} =\left(\mathrm{2}{k}+\mathrm{4}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\mathrm{4}{k}^{\mathrm{2}} +\mathrm{4}{k}^{\mathrm{2}} +\mathrm{8}{k}+\mathrm{4}=\mathrm{4}{k}^{\mathrm{2}}…
Question Number 111046 by Algoritm last updated on 01/Sep/20 Commented by Her_Majesty last updated on 02/Sep/20 $$\mathrm{80} \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 111044 by mathdave last updated on 01/Sep/20 Commented by kaivan.ahmadi last updated on 01/Sep/20 $$\mathrm{5}. \\ $$$${a}\mid{m},{b}\mid{m}\Rightarrow{ab}\mid{m}\:{on}\:{the}\:{other}\:{hand} \\ $$$${lcm}\left({a},{b}\right)\mid{ab}\:{so}\:{lcm}\left({a},{b}\right)\mid{m}. \\ $$$$\mathrm{6}. \\ $$$${let}\:{a},{b}\in\mathbb{R}…
Question Number 111043 by mathdave last updated on 01/Sep/20 $${solve}\:{the}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\:\sqrt{{x}}\left(\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} \right)^{\frac{\mathrm{3}}{\mathrm{4}}} }{dx} \\ $$ Terms of Service Privacy Policy Contact:…