Category: Limits

Question Number 76815 by Rio Michael last updated on 30/Dec/19 $$\mathrm{Which}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{series}\mathrm{is}\mathbf{N}\mathrm{o}\mathbf{t}\mathrm{convergent}?$$$$\mathrm{A}.\underset{\mathrm{r}=1}{\sum ^{\mathrm{\infty }}}\frac{1}{{\mathrm{r}}^3}$$$$\mathrm{B}.\underset{\mathrm{r}=1}{\sum ^{\mathrm{\infty }}}\frac{1}{{\mathrm{r}}^2}$$$$\mathrm{C}.\:\underset{\mathrm{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{r}^{\mathrm{2}}…

Question Number 142329 by HarshSahu last updated on 30/May/21 $${lim}_{x\to \mathrm{\infty }}{\left(\frac{x!}{x^x}\right)}^{\frac{1}{x}}$$ Answered by Dwaipayan Shikari last updated on 30/May/21 $$\left(\frac{{x}!}{{x}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}} ={y}…

Question Number 142308 by qaz last updated on 29/May/21 $$\underset{\mathrm{x}\to 0}{\lim }\frac{\mathrm{lnlnln}[\mathrm{x}+{(1+\mathrm{x})}^{\frac{{(1+\mathrm{x})}^{\frac{1}{\mathrm{x}}}}{\mathrm{x}}}]+\mathrm{x}(1-\frac{1}{{\mathrm{e}}^{\mathrm{e}+1}})}{{\mathrm{x}}^2}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 142300 by qaz last updated on 29/May/21 $$\underset{\mathrm{x}\to 0}{\lim }\frac{{({\mathrm{e}}^{\sin \mathrm{x}}+\sin \mathrm{x})}^{\frac{1}{\sin \mathrm{x}}}-{({\mathrm{e}}^{\tan \mathrm{x}}+\tan \mathrm{x})}^{\frac{1}{\tan \mathrm{x}}}}{{\mathrm{x}}^3}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 142277 by liberty last updated on 29/May/21 $$\underset{x\to 0}{\lim }\frac{1-e^{\sin x\ln \left(\cos x\right)}}{x^3}=?$$ Answered by Dwaipayan Shikari last updated on 29/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−{e}^{{sinx}\left(−\frac{{x}^{\mathrm{2}}…