Category: Limits

Question Number 144946 by mnjuly1970 last updated on 30/Jun/21 $$$$$$\mathit{\varphi }:={\int }_0^{\frac{\pi }{2}}{\left(\frac{\mathrm{x}}{\cot \left(\mathrm{x}\right)}\right)}^3\mathrm{dx}=?$$$$$$ Terms of Service Privacy Policy Contact:…

Question Number 79374 by TawaTawa last updated on 24/Jan/20 Answered by mind is power last updated on 24/Jan/20 $$cv\sim \frac{1}{n^2}Riemann$$$$\frac{n-1}{(n+1)(n+2)(n+3)}=\frac{1}{n+1}+\frac{-3}{-1.1.(n+2)}-\frac{4}{(-2)(-1)(n+3)}$$$$=\underset{{n}\geqslant\mathrm{1}} {\sum}\left\{−\frac{\mathrm{1}}{{n}+\mathrm{1}}+\frac{\mathrm{3}}{\left({n}+\mathrm{2}\right)}−\frac{\mathrm{2}}{\left({n}+\mathrm{3}\right)}\right\}…

Question Number 79360 by TawaTawa last updated on 24/Jan/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 144816 by liberty last updated on 29/Jun/21 $$\underset{x\to 0}{\lim }\frac{\sqrt{1+{6\mathrm{x}}^2}-(1+7\mathrm{x})}{{\mathrm{x}}^2(\mathrm{x}-3)}=?$$ Answered by imjagoll last updated on 29/Jun/21 $$\:=−\frac{\mathrm{1}}{\mathrm{3}}\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{6x}^{\mathrm{2}} \right)−\left(\mathrm{1}+\mathrm{14x}+\mathrm{49x}^{\mathrm{2}}…

Question Number 79236 by jagoll last updated on 23/Jan/20 $$\underset{x\to +\mathrm{\infty }}{\lim }\mathrm{x}\{\mathrm{e}-{(1+\frac{1}{\mathrm{x}})}^{\mathrm{x}}\}=?$$ Commented by mathmax by abdo last updated on 23/Jan/20 $${let}\:{A}\left({x}\right)={x}\left\{{e}−\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} \right\}\:\:{we}\:{have}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}}…