Category: Limits

Question Number 163657 by mathlove last updated on 09/Jan/22 $$\underset{x\to 0}{\lim }\frac{{(1+x)}^{\frac{1}{x}}-e}{x}=?$$ Answered by mr W last updated on 09/Jan/22 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left({e}^{\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}\right)}{{x}}} \right)'…

Question Number 98114 by malwaan last updated on 11/Jun/20 $$1\underset{\mathit{x}\to \mathrm{\infty }}{\mathit{l}\mathit{i}\mathit{m}}{}^3\sqrt{5{\mathit{x}}^3}=?$$$$2\underset{\mathit{x}\to \mathrm{\infty }}{\mathit{l}\mathit{i}\mathit{m}}{(1+\frac{\mathit{n}}{\mathit{x}+\mathit{\alpha }})}^{\mathit{x}};\mathit{\alpha }\mathit{i}\mathit{s}\mathit{c}\mathit{o}\mathit{n}\mathit{s}\mathit{t}\mathit{a}\mathit{n}\mathit{t}$$ Answered by mahdi last updated on…

Question Number 163642 by cortano1 last updated on 09/Jan/22 $$\underset{x\to \frac{2}{3}}{\lim }\frac{\lfloor 3x\rfloor -3x}{9x^2-4}=?$$ Answered by mehdiAz last updated on 09/Jan/22 $$$$$$\:\:\:\:\:\:\underset{{x}\rightarrow\frac{\mathrm{2}}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\lfloor\mathrm{3}{x}\rfloor−\mathrm{3}{x}}{\mathrm{9}{x}^{\mathrm{2}}…

Question Number 163608 by qaz last updated on 08/Jan/22 $${\mathrm{A}}_{\mathrm{n}}=\frac{\mathrm{n}}{{\mathrm{n}}^2+1^2}+\frac{\mathrm{n}}{{\mathrm{n}}^2+2^2}+\dots +\frac{\mathrm{n}}{{\mathrm{n}}^2+{\mathrm{n}}^2}$$$$\mathrm{Prove}::\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{1}{{\mathrm{n}}^4\{\frac{1}{24}-\mathrm{n}[\mathrm{n}(\frac{\pi }{4}-{\mathrm{A}}_{\mathrm{n}})-\frac{1}{4}]\}}=2016$$ Terms…

Question Number 163582 by mathlove last updated on 08/Jan/22 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{7^{x+2}+6^x}{3^{2x}-5^x}=?$$ Answered by cortano1 last updated on 08/Jan/22 $$\:\underset{{x}\rightarrow\infty}…