Category: Limits

Question Number 103313 by gui last updated on 14/Jul/20 $${li}\underset{{n}\rightarrow+\infty} {{m}}\left(\mathrm{ln}\:\left({n}!\right)\right)^{\frac{\mathrm{2}}{{n}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

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 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 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 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}}…