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Category: Limits

bobhans-find-without-L-Hopital-and-series-lim-x-0-x-sin-x-x-3-

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…

lim-x-0-x-2-pi-1-1-2-1-2-2-1-3-3-1-x-1-solve-this-pleas-

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-107222

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-107163

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)}=…

lim-x-0-2-3-x-1-4x-2-

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 \\…

bemath-lim-x-2-3x-1-4x-2-

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}=…

Evaluate-k-1-2n-1-1-k-1-k-3-

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}}…