Category: Limits

Question Number 200304 by Calculusboy last updated on 16/Nov/23 Answered by Sutrisno last updated on 17/Nov/23 $${lim}_{n\to \mathrm{\infty }}0.2^{{log}_{\sqrt{5}}\left(\frac{\frac{1}{4}}{1-\frac{1}{2}}\right)}$$$${lim}_{n\to \mathrm{\infty }}0.2^{{log}_{\sqrt{5}}\left(\frac{1}{3}\right)}$$$${lim}_{{n}\rightarrow\infty}…

Question Number 200298 by Calculusboy last updated on 16/Nov/23 Commented by Frix last updated on 17/Nov/23 $$-\frac{1}{16}$$ Answered by Rasheed.Sindhi last updated on…

Question Number 200105 by cortano12 last updated on 14/Nov/23 Commented by mr W last updated on 14/Nov/23 Commented by mr W last updated on 14/Nov/23…

Question Number 199983 by cortano12 last updated on 11/Nov/23 $$\mathrm{find}\underset{x\to \mathrm{\infty }}{\lim }\sin \left(\frac{\pi \mathrm{x}}{5+3\mathrm{x}}\right)$$$$\mathrm{by}\mathrm{sequeeze}\mathrm{theorem}$$ Answered by tri26112004 last updated on 12/Nov/23 $$Wehave$$$$\mid{sin}\left(\:\frac{\pi{x}}{\mathrm{5}+\mathrm{3}{x}}\right)\mid\:\leqslant\:\mathrm{1}…

Question Number 199843 by universe last updated on 10/Nov/23 $$\underset{x\to 0}{\lim }(\frac{1}{\ln (1+x)}-\frac{1}{\ln (x+\sqrt{1+x^2})})=??$$ Answered by witcher3 last updated on 10/Nov/23 $$=\frac{\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)−\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{ln}\left(\left(\mathrm{1}+\mathrm{x}\right)\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)\right.}= \…