Category: Limits

Question Number 103114 by Study last updated on 12/Jul/20 Commented by Study last updated on 12/Jul/20 $$rightorwrong?$$ Commented by Ari last updated on…

Question Number 168575 by qaz last updated on 13/Apr/22 $$\mathrm{Calculate}::\underset{\mathrm{x}\to +\mathrm{\infty }}{\lim }\frac{{(\mathrm{x}+\mathrm{a})}^{\mathrm{x}+\mathrm{a}}{(\mathrm{x}+\mathrm{b})}^{\mathrm{x}+\mathrm{b}}}{{(\mathrm{x}+\mathrm{a}+\mathrm{b})}^{2\mathrm{x}+\mathrm{a}+\mathrm{b}}}=?$$ Answered by LEKOUMA last updated on 14/Apr/22 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{{x}^{{x}+{a}}…

Question Number 168464 by Altaf180 last updated on 11/Apr/22 $$li\underset{x\to 0}{m}\frac{1-cos7x}{x^2}=?$$ Commented by safojontoshtemirov last updated on 11/Apr/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}2}\left({sin}^{\mathrm{2}} \frac{\mathrm{7}{x}}{\mathrm{2}}\right)/{x}^{\mathrm{2}} =\underset{{x}\rightarrow\mathrm{0}}…

Question Number 168256 by mathlove last updated on 07/Apr/22 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{n!}{n^n}=?$$ Answered by MJS_new last updated on 07/Apr/22 $$\mathrm{first}\mathrm{thought}\frac{n!}{n^n}\mathrm{means}\frac{1\times 2\times \dots \times n}{n\times n\times \dots \times n}\mathrm{means}$$$$\frac{{n}−\mathrm{1}\:{numbers}\:{smaller}\:{than}\:{n}}{{n}−\mathrm{1}\:{times}\:{n}}\:\mathrm{which}\:\mathrm{looks}…

Question Number 168166 by cortano1 last updated on 05/Apr/22 $$\underset{x\to 0}{\lim }\frac{\sin \left(\sin x\right)-x\sqrt[3]{1-x}}{x^5}=?$$ Answered by qaz last updated on 05/Apr/22 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\mathrm{sin}\:\mathrm{x}\right)−\mathrm{x}\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{x}}}{\mathrm{x}^{\mathrm{5}} } \…