Question Number 121042 by bramlexs22 last updated on 05/Nov/20 $$\mathrm{prove}\:\mathrm{that}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} =\:\mathrm{e}\: \\ $$ Answered by bobhans last updated on 05/Nov/20 $${Let}\:{w}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} \\ $$$${then}\:\mathrm{ln}\:\left({w}\right)=\:\mathrm{ln}\:\left(\underset{{x}\rightarrow\infty}…
Question Number 121031 by bramlexs22 last updated on 05/Nov/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}+\:\mid\mathrm{x}\mid\:\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{x}}.\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)? \\ $$ Commented by liberty last updated on 05/Nov/20 $$\:\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{\mathrm{x}+\mid\mathrm{x}\mid\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{x}}.\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\: \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}^{−}…
Question Number 55491 by Tinkutara last updated on 25/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 26/Feb/19 $${trying}\:{to}\:\:{understand}\: \\ $$$${restricting}\:{under}\:{following}\:{condition} \\ $$$$\left.\mathrm{1}\right){radius}\left({r}\right)\:{taken}\:{as}\:{integer} \\ $$$$\left.\mathrm{2}\right){centre}\:{and}\:{otherpoints}\:\boldsymbol{{lie}}\:\boldsymbol{{on}}\:\boldsymbol{{the}}\:\boldsymbol{{circle}} \\ $$$$\boldsymbol{{not}}\:\boldsymbol{{counted}}\:\boldsymbol{{in}}\:\boldsymbol{{f}}\left(\boldsymbol{{r}}\right)…
Question Number 121010 by mathocean1 last updated on 04/Nov/20 $$\mathrm{calculate}: \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\:\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{2}}{\mathrm{3}−\sqrt{\mathrm{x}+\mathrm{6}}} \\ $$ Answered by 675480065 last updated on 04/Nov/20 $$=\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}+\mathrm{1}}}}{−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}+\mathrm{6}}}}=−\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\sqrt{\frac{\mathrm{x}+\mathrm{6}}{\mathrm{x}+\mathrm{1}}}=−\mathrm{3}/\mathrm{2}…
Question Number 55373 by gunawan last updated on 23/Feb/19 $$\underset{{n}\rightarrow\propto} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} {e}^{{x}^{{n}} } }{\mathrm{cos}\:{x}}\:{dx}=… \\ $$ Commented by turbo msup by abdo last…
Question Number 55334 by Mikael_Marshall last updated on 21/Feb/19 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{8}^{{n}} }{\mathrm{2}^{{n}+\mathrm{1}} +\mathrm{3}^{{n}+\mathrm{2}} } \\ $$ Answered by mr W last updated on 21/Feb/19 $$=\underset{{n}\rightarrow\infty}…
Question Number 120862 by bemath last updated on 03/Nov/20 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{2}}{\mathrm{x}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{1}}{\mathrm{sec}\:\left(\frac{\mathrm{3}}{\mathrm{x}}\right)\:\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{x}}\right)}\:? \\ $$ Commented by liberty last updated on 03/Nov/20 $$\mathrm{take}\:\mathrm{X}=\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{then}\:\:\underset{\mathrm{X}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2X}−\mathrm{cos}\:\mathrm{X}+\mathrm{1}}{\mathrm{sec}\:\mathrm{3X}.\:\mathrm{tan}\:^{\mathrm{2}}…
Question Number 120843 by bramlexs22 last updated on 03/Nov/20 $$\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}+\mathrm{9}−\mathrm{6}\sqrt{\mathrm{x}}}}{\:\sqrt{\mathrm{x}}−\mathrm{3}}\:? \\ $$ Commented by Dwaipayan Shikari last updated on 03/Nov/20 $$\frac{\sqrt{\mathrm{12}−\mathrm{6}\sqrt{\mathrm{3}}}}{\:\sqrt{\mathrm{3}}−\mathrm{3}}=−\mathrm{1} \\ $$ Answered…
Question Number 120823 by bramlexs22 last updated on 03/Nov/20 Answered by liberty last updated on 03/Nov/20 $$\:\rho\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{cos}\:\mathrm{x}+\sqrt{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{x}^{\mathrm{3}} }}−\mathrm{1}}{\mathrm{xsin}\:\mathrm{x}} \\ $$$$\:\rho=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:\mathrm{x}−\mathrm{1}\right)+\sqrt{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{x}^{\mathrm{3}} }}{\mathrm{x}\:\mathrm{sin}\:\mathrm{x}}\:.\left(\frac{\mathrm{1}}{\mathrm{2}}\right)…
Question Number 186327 by cortano1 last updated on 03/Feb/23 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{2}}{\mathrm{3}}{x}^{\mathrm{4}} +{x}^{\mathrm{2}} −\mathrm{tan}\:^{\mathrm{2}} {x}}{{x}^{\mathrm{6}} }\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com