Category: Limits

Question Number 203508 by Fridunatjan08 last updated on 20/Jan/24 $$Evaluatethegivenlimit:$$$$\underset{n\to \mathrm{\infty }}{lim}\frac{\sqrt[n]{8}-1}{\sqrt[n]{16}-1}$$ Answered by esmaeil last updated on 20/Jan/24 $$=Y$$$$\frac{\mathrm{1}}{{n}}={p}\rightarrow\left({n}\rightarrow\infty\rightarrow{p}\rightarrow\mathrm{0}\right)…

Question Number 203247 by mathlove last updated on 13/Jan/24 $$\underset{x\to 0}{\lim }xtan\frac{\pi }{2}(1+x)=?$$ Answered by MM42 last updated on 13/Jan/24 $$={lim}_{x\to 0}-xcot\frac{\pi }{2}x={lim}_{x\to 0}-\frac{\frac{\pi }{2}xcos\frac{\pi }{2}x}{sin\frac{\pi }{2}x}\times \frac{2}{\pi }$$$$=\:−\frac{\mathrm{2}}{\pi}\:\checkmark…

Question Number 203059 by hassanmpsy last updated on 08/Jan/24 Commented by witcher3 last updated on 11/Jan/24 $$\mathrm{U}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}\left(\mathrm{1}+\frac{\mathrm{k}}{\mathrm{n}}\right)}{\mathrm{n}^{\mathrm{2}} \left(\mathrm{2}+\mathrm{2}\frac{\mathrm{k}}{\mathrm{n}}+\left(\frac{\mathrm{k}}{\mathrm{n}}\right)^{\mathrm{2}} \right)}=\frac{\mathrm{1}}{\mathrm{n}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{f}\left(\frac{\mathrm{k}}{\mathrm{n}}\right) \…

Question Number 202249 by cortano12 last updated on 23/Dec/23 $$\mathrm{C}=\underset{x\to 0}{\lim }\frac{\mathrm{x}\sqrt[3]{\cos \mathrm{x}}-\sin \mathrm{x}}{{\mathrm{x}}^5}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 202161 by Calculusboy last updated on 22/Dec/23 Answered by som(math1967) last updated on 22/Dec/23 $$\frac{(m+1)!(1+3+5+\dots +2m+3}{2m(m+2)(1+2+3+\dots +m+1)}$$$$=\frac{(m+1)!\frac{m+2}{2}\times 2\{1+(m+2-1)\}}{2m(m+2)\frac{(m+1)(m+2)}{2}}$$$$=\frac{(m+1)!{(m+2)}^2}{m{(m+2)}^2(m+1)}$$$$=\frac{{m}\left({m}+\mathrm{1}\right)×\left({m}−\mathrm{1}\right)!}{{m}\left({m}+\mathrm{1}\right)}…