Category: Limits

Question Number 50395 by Abdo msup. last updated on 16/Dec/18 $$let{U}_n={(e-{(1+\frac{1}{n})}^n)}^{\sqrt{n^2+2}-\sqrt{n^2+1}}$$$$calculate{lim}_{n\to +\mathrm{\infty }}{U}_n$$ Terms of Service Privacy Policy…

Question Number 115889 by bemath last updated on 29/Sep/20 $$\underset{x\to 0}{\lim }\frac{\sqrt[3]{1+\cos 2x}-\sqrt[3]{2}}{x^2.\sin 3x}$$ Answered by bemath last updated on 29/Sep/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{1}+\left(\mathrm{1}−\frac{\mathrm{4}{x}^{\mathrm{2}} }{\mathrm{2}}\right)}−\sqrt[{\mathrm{3}\:}]{\mathrm{2}}}{{x}^{\mathrm{2}} .\mathrm{sin}\:\mathrm{3}{x}}\:=…

Question Number 115780 by bemath last updated on 28/Sep/20 $$\underset{x\to 0}{\lim }{\left(\cos x\right)}^{\frac{1}{x^2}}=?$$$$\underset{x\to \mathrm{\infty }}{\lim }{(e^{3x}-5x)}^{\frac{1}{x}}=?$$$$\underset{x\to 0}{\lim }\frac{e^{2x}-2e^x+1}{\cos 3x-2\cos 2x+\cos x}=?$$$$\underset{{x}\rightarrow\mathrm{0}}…

Question Number 115775 by bemath last updated on 28/Sep/20 $$\underset{x\to \mathrm{\infty }}{\lim }\sqrt[3]{\frac{(3-\sqrt{x})(\sqrt{x}+2)}{8x-4}}$$ Answered by bobhans last updated on 28/Sep/20 $$\underset{x\to \mathrm{\infty }}{\lim }\sqrt[3]{\frac{(3-\sqrt{x})(\sqrt{x}+2)}{8x-4}}=\sqrt[3]{\underset{x\to \mathrm{\infty }}{\lim }\frac{6+\sqrt{x}-x}{8x-4}}$$$$=\sqrt[{\mathrm{3}\:}]{\underset{{x}\rightarrow\infty}…

Question Number 115621 by sachin1221 last updated on 27/Sep/20 $$$$$$\dots advancedcalculus\dots$$$$evaluate::$$$$showthat{lim}_{n\to \mathrm{\infty }}\frac{1}{n}[{cos}^{2p}\frac{\pi }{2n}+{cos}^{2p}\frac{2\pi }{2n}+{cos}^{2p}\frac{3\pi }{2n}\dots \dots {cos}^{2p}\frac{\pi }{2}]=\underset{r=1}{\prod ^p}\frac{p+r}{4r}$$…