Question Number 102763 by Ar Brandon last updated on 10/Jul/20 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{defined}\:\mathrm{within}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\mathrm{by}\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{1}\:\mathrm{if}\:\mathrm{x}\in\mathbb{Q}\cap\left[\mathrm{0},\mathrm{1}\right]}\\{\mathrm{0}\:\mathrm{otherwise}}\end{cases}\:\:\mathrm{is}\:\mathrm{not}\:\mathrm{Riemann}\:\mathrm{integrable} \\ $$$$\mathrm{within}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 168256 by mathlove last updated on 07/Apr/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{n}!}{{n}^{{n}} }=? \\ $$ Answered by MJS_new last updated on 07/Apr/22 $$\mathrm{first}\:\mathrm{thought}\:\frac{{n}!}{{n}^{{n}} }\:\mathrm{means}\:\frac{\mathrm{1}×\mathrm{2}×…×{n}}{{n}×{n}×…×{n}}\:\mathrm{means} \\ $$$$\frac{{n}−\mathrm{1}\:{numbers}\:{smaller}\:{than}\:{n}}{{n}−\mathrm{1}\:{times}\:{n}}\:\mathrm{which}\:\mathrm{looks}…
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Question Number 168166 by cortano1 last updated on 05/Apr/22 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)−{x}\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}}}{{x}^{\mathrm{5}} }\:=? \\ $$ Answered by qaz last updated on 05/Apr/22 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\mathrm{sin}\:\mathrm{x}\right)−\mathrm{x}\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{x}}}{\mathrm{x}^{\mathrm{5}} } \\…
Question Number 168147 by qaz last updated on 04/Apr/22 $$\mathrm{calculate}\:\:::\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\sqrt[{\mathrm{x}^{\mathrm{3}} }]{\frac{\mathrm{tan}\:\left(\mathrm{1}+\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{tan}\:\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)}}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 168144 by cortano1 last updated on 04/Apr/22 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}} \sqrt{\mathrm{1}+{x}}\:−\mathrm{sin}\:^{\mathrm{3}} {x}\:−\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{3}} \:\mathrm{tan}\:{x}}{\left(\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{2}{x}^{\mathrm{3}} }−\mathrm{1}\right)\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}=?\:\:\:\:\:\:\:\: \\ $$ Answered by qaz last updated on 05/Apr/22…
Question Number 168143 by cortano1 last updated on 04/Apr/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{{x}^{\mathrm{4}} }\:=?\:\:\:\:\:\: \\ $$ Answered by qaz last updated on 04/Apr/22 $$ \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}}…
Question Number 168055 by qaz last updated on 01/Apr/22 $$\mathrm{Calculate}\:::\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\mathrm{x}\right)^{−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }} }{\mathrm{x}}=? \\ $$ Answered by LEKOUMA last updated on 03/Apr/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\left(\left(\mathrm{1}+{x}\right)−\mathrm{1}\right)\frac{\mathrm{1}}{{x}^{\mathrm{3}} }}…
Question Number 102510 by Study last updated on 09/Jul/20 $${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{sin}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{3}}{x}+\frac{\mathrm{1}}{\mathrm{3}}\bigtriangleup{x}\right)−{sin}^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{3}}{x}}{\bigtriangleup{x}}=? \\ $$ Answered by bemath last updated on 09/Jul/20 $$\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{3}}\left({x}+\Delta{x}\right)−\mathrm{sin}\:^{\mathrm{2}}…
Question Number 102508 by Study last updated on 09/Jul/20 $${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{e}^{{sin}\left({x}−\bigtriangleup{x}\right)} −{e}^{{sinx}} }{\bigtriangleup{x}}=? \\ $$ Commented by bemath last updated on 09/Jul/20 $${may}\:{be}\:\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{sin}\:\left({x}+\Delta{x}\right)} −{e}^{\mathrm{sin}\:{x}}…