Question Number 103255 by Study last updated on 13/Jul/20 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\left(\frac{{sin}^{\mathrm{6}} \sqrt{\mathrm{2}}{x}}{{tan}^{\mathrm{7}} \frac{{x}}{\mathrm{2}}}\right)^{{cos}^{\mathrm{12}} {x}} =??? \\ $$ Commented by Dwaipayan Shikari last updated on 13/Jul/20…
Question Number 168776 by safojontoshtemirov last updated on 17/Apr/22 Commented by Oktamboy last updated on 17/Apr/22 $${Stirling} \\ $$ Commented by infinityaction last updated on…
Question Number 168696 by qaz last updated on 16/Apr/22 $$\mathrm{Calculate}\:\:\:::\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\mathrm{2x}−\mathrm{1}} ^{\mathrm{2x}+\mathrm{1}} \mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \mathrm{dt}−\int_{−\mathrm{1}} ^{\mathrm{1}} \mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \mathrm{dt}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{8e}\:\:\:,\mathrm{Don}'\mathrm{t}\:\mathrm{use}\:\mathrm{L}'\mathrm{Hospital}'\mathrm{s}\:\mathrm{rule}. \\ $$ Answered by aleks041103…
Question Number 103114 by Study last updated on 12/Jul/20 Commented by Study last updated on 12/Jul/20 $${right}\:{or}\:{wrong}? \\ $$ Commented by Ari last updated on…
Question Number 168576 by cortano1 last updated on 13/Apr/22 $$\:\:\:{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:^{{m}} \left({mx}\right)−\mathrm{cos}\:^{{n}} \left({nx}\right)}{\left({m}^{\mathrm{2}} +{n}^{\mathrm{2}} +{mn}\right){x}^{\mathrm{2}} \:}\:=\:\mathrm{1} \\ $$$$\:{find}\:\frac{{m}^{\mathrm{2}} +{n}^{\mathrm{2}} −\mathrm{4}}{{mn}}\:. \\ $$ Commented by blackmamba…
Question Number 168575 by qaz last updated on 13/Apr/22 $$\mathrm{Calculate}\:::\:\:\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}}\frac{\left(\mathrm{x}+\mathrm{a}\right)^{\mathrm{x}+\mathrm{a}} \left(\mathrm{x}+\mathrm{b}\right)^{\mathrm{x}+\mathrm{b}} }{\left(\mathrm{x}+\mathrm{a}+\mathrm{b}\right)^{\mathrm{2x}+\mathrm{a}+\mathrm{b}} }=? \\ $$ Answered by LEKOUMA last updated on 14/Apr/22 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{{x}^{{x}+{a}}…
Question Number 168555 by mathlove last updated on 13/Apr/22 Answered by LEKOUMA last updated on 13/Apr/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−{x}^{\mathrm{2}} −\frac{{x}^{\mathrm{4}} }{\mathrm{3}}+{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} }=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−{x}^{\mathrm{4}} }{\mathrm{3}{x}^{\mathrm{4}} }=−\frac{\mathrm{1}}{\mathrm{3}}…
Question Number 168464 by Altaf180 last updated on 11/Apr/22 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{\mathrm{1}−{cos}\mathrm{7}{x}}{{x}^{\mathrm{2}} }=? \\ $$ Commented by safojontoshtemirov last updated on 11/Apr/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}2}\left({sin}^{\mathrm{2}} \frac{\mathrm{7}{x}}{\mathrm{2}}\right)/{x}^{\mathrm{2}} =\underset{{x}\rightarrow\mathrm{0}}…
Question Number 102763 by Ar Brandon last updated on 10/Jul/20 $$\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}…