Question Number 107299 by bobhans last updated on 10/Aug/20 $$\:\:\:\:\:\:\maltese\mathrm{bobhans}\maltese \\ $$$$\mathrm{find}\:\mathrm{without}\:\mathrm{L}'\mathrm{Hopital}\:\mathrm{and}\:\mathrm{series}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:? \\ $$ Answered by john santu last updated on…
Question Number 41761 by math khazana by abdo last updated on 12/Aug/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:{x}\:{ln}\left(\mathrm{1}−{e}^{{sinx}} \right)\: \\ $$ Answered by alex041103 last updated on 12/Aug/18 $${As}\:{x}\rightarrow\mathrm{0}\:{the}\:{expression}\:{becomes}\:{one}…
Question Number 172766 by mathlove last updated on 01/Jul/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}!!−\sqrt{\frac{\mathrm{2}}{\pi}}}{\left(\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }+\centerdot\centerdot\centerdot\right)−\Psi_{\mathrm{1}} \left({x}+\mathrm{1}\right)}=? \\ $$$${solve}\:{this}\:{pleas} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 107222 by bobhans last updated on 09/Aug/20 Answered by john santu last updated on 09/Aug/20 $$\:\:\:\:\:\:\:\boxdot\mathrm{JS}\boxdot \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{7}^{\mathrm{2x}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{x}} }\right)\right)^{\frac{\mathrm{2}}{\mathrm{x}}} =\:\mathrm{7}^{\mathrm{4}} \:×\underset{{x}\rightarrow\infty}…
Question Number 107207 by bemath last updated on 09/Aug/20 $$\:\:\:\:\:\circledcirc{bemath}\circledcirc \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}^{{x}} +\mathrm{3}^{{x}} \right)^{\frac{\mathrm{1}}{{x}}} \:?\: \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 172715 by mathlove last updated on 30/Jun/22 $$\Omega=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{ln}\left({x}!\right)}{\:\sqrt[{{x}}]{\mathrm{1}+{x}}−{e}}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107163 by bobhans last updated on 09/Aug/20 Answered by john santu last updated on 09/Aug/20 $$\:\:\:\trianglerighteq\mathrm{JS}\trianglelefteq \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{cos}\:\mathrm{x}\:.\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}\sqrt{\mathrm{1}+\frac{\mathrm{5}}{\mathrm{x}}}}{\mathrm{2}\left(\sqrt[{\mathrm{5}}]{\mathrm{1}−\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{8}}}−\mathrm{1}\right)}= \\ $$$$\mathrm{1}\:×\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}\sqrt{\mathrm{1}+\frac{\mathrm{5}}{\mathrm{x}}}}{\mathrm{2}\left(\mathrm{1}−\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{40}}−\mathrm{1}\right)}=…
Question Number 107030 by bemath last updated on 08/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{2}+\frac{\mathrm{3}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{4}{x}−\mathrm{2}}} \\ $$ Commented by kaivan.ahmadi last updated on 08/Aug/20 $${y}=\left(\mathrm{2}+\frac{\mathrm{3}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{4}{x}−\mathrm{2}}} \Rightarrow{lim}_{{x}\rightarrow\infty} {lny}={lim}_{{x}\rightarrow\infty} \frac{{ln}\left(\mathrm{2}+\frac{\mathrm{3}}{{x}}\right)}{\mathrm{4}{x}−\mathrm{2}}\sim \\…
Question Number 107028 by bemath last updated on 08/Aug/20 $$\:\:\:@{bemath}@ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}+\mathrm{3}{x}\right)^{\frac{\mathrm{1}}{\mathrm{4}{x}−\mathrm{2}}} \\ $$ Commented by kaivan.ahmadi last updated on 08/Aug/20 $${y}=\left(\mathrm{2}+\mathrm{3}{x}\right)^{\frac{\mathrm{1}}{\mathrm{4}{x}−\mathrm{2}}} \Rightarrow{lny}=\frac{{ln}\left(\mathrm{2}+\mathrm{3}{x}\right)}{\mathrm{4}{x}−\mathrm{2}}\Rightarrow{lim}_{{x}\rightarrow\infty} {lny}=…
Question Number 41454 by Fawomath last updated on 07/Aug/18 $$\mathrm{Evaluate}\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} {k}^{\mathrm{3}} \\ $$ Commented by maxmathsup by imad last updated on 07/Aug/18 $${let}\:{S}\left({x}\right)=\sum_{{k}=\mathrm{0}}…