Question Number 129640 by Yashvi last updated on 17/Jan/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129584 by bemath last updated on 16/Jan/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{sin}\:\mathrm{x}\right)\left(\mathrm{arctan}\:\mathrm{x}\right)−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{x}^{\mathrm{2}} \right)}=? \\ $$ Answered by liberty last updated on 16/Jan/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}}+\frac{\mathrm{x}^{\mathrm{5}}…
Question Number 129587 by Adel last updated on 16/Jan/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} =? \\ $$ Answered by Dwaipayan Shikari last updated on 16/Jan/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right)^{{x}} =\underset{{x}\rightarrow\infty}…
Question Number 64047 by aliesam last updated on 12/Jul/19 Commented by mathmax by abdo last updated on 12/Jul/19 $${we}\:{have}\:{x}_{\mathrm{0}} =\mathrm{1}\:{and}\:{x}_{{n}+\mathrm{1}} =\frac{\mathrm{3}+\mathrm{2}{x}_{{n}} }{\mathrm{3}+{x}_{{n}} }\:\Rightarrow{x}_{{n}+\mathrm{1}} ={f}\left({x}_{{n}} \right)\:{with}…
Question Number 129510 by Adel last updated on 16/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{log}\:\mathrm{x}} =? \\ $$ Commented by mr W last updated on 16/Jan/21 $$\Rightarrow{Q}\mathrm{129387} \\ $$…
Question Number 63964 by meme last updated on 11/Jul/19 $${li}\underset{{x}\rightarrow+\infty} {{m}e}^{−{xln}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right)} \\ $$ Commented by Prithwish sen last updated on 11/Jul/19 $$\mathrm{li}\underset{\mathrm{x}\rightarrow\infty} {\mathrm{m}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} \rightarrow\:\mathrm{e}^{−\mathrm{1}} \\…
Question Number 63959 by meme last updated on 11/Jul/19 $${li}\underset{{x}\rightarrow+\infty} {{m}e}^{{xln}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)} \\ $$ Commented by Prithwish sen last updated on 11/Jul/19 $$\:\mathrm{li}\underset{\mathrm{x}\rightarrow\infty} {\mathrm{m}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} \rightarrow\:\mathrm{e} \\…
Question Number 63921 by raj last updated on 11/Jul/19 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\left(\frac{{n}}{{n}+\mathrm{1}}\right)^{\alpha} +\mathrm{sin}\:\frac{\mathrm{1}}{{n}}\right)^{{n}} \mathrm{where}\:\alpha\in\mathbb{Q} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Commented by kaivan.ahmadi last updated on 11/Jul/19 $$\sim{lim}_{{n}\rightarrow\infty}…
Question Number 63922 by raj last updated on 11/Jul/19 $$\mathrm{if}\:{f}\left({x}\right)=\begin{cases}{\frac{\mathrm{log}\:\left(\mathrm{1}+\mathrm{2}{ax}\right)−\mathrm{log}\:\left(\mathrm{1}−{bx}\right)}{{x}}}&{{x}\neq\mathrm{0}}\\{{k}}&{{x}=\mathrm{0}}\end{cases} \\ $$$$\mathrm{is}\:\mathrm{continuous}\:\mathrm{at}\:{x}=\mathrm{0}\:\mathrm{then}\:{k}=? \\ $$ Commented by kaivan.ahmadi last updated on 11/Jul/19 $${lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right)\overset{{hop}} {=}{lim}_{{x}\rightarrow\mathrm{0}\:\:} \frac{\mathrm{2}{a}}{{ln}\mathrm{10}×\left(\mathrm{1}+\mathrm{2}{ax}\right)}−\frac{−{b}}{{ln}\mathrm{10}×\left(\mathrm{1}−{bx}\right)}=…
Question Number 63919 by raj last updated on 11/Jul/19 $$\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)=? \\ $$ Commented by Prithwish sen last updated on 11/Jul/19 $$\underset{\mathrm{n}=\mathrm{2}} {\overset{\mathrm{n}=\boldsymbol{\mathrm{n}}}…