Category: Limits

Question Number 196959 by cortano12 last updated on 05/Sep/23 $$\underset{―}{}$$ Answered by horsebrand11 last updated on 05/Sep/23 $$\:\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{sin}\:\mathrm{2x}−\mathrm{2x}}{\mathrm{x}^{\mathrm{3}} }\:\right)+\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{ax}+\mathrm{2x}}{\mathrm{x}^{\mathrm{3}} }\right)=\mathrm{1}−\mathrm{b}…

Question Number 196534 by cortano12 last updated on 27/Aug/23 $$\underset{x\to \mathrm{\infty }}{\lim }\mathrm{x}\sqrt{1-\cos \left(\frac{\pi }{\mathrm{x}}\right)}=?$$ Answered by Mathspace last updated on 27/Aug/23 $$1-cosu\sim \frac{u^2}{2}(u\to o)\Rightarrow$$$$\mathrm{1}−{cos}\left(\frac{\pi}{{x}}\right)\sim\frac{\pi^{\mathrm{2}} }{\mathrm{2}{x}^{\mathrm{2}}…

Question Number 196471 by Tawa11 last updated on 25/Aug/23 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{1}{\mathrm{n}}(\frac{1}{2+\frac{1}{\mathrm{n}}}+\frac{1}{2+\frac{2}{\mathrm{n}}}+\frac{1}{2+\frac{3}{\mathrm{n}}}+..+\frac{1}{2+\frac{\mathrm{n}}{\mathrm{n}}})$$ Answered by mr W last updated on 25/Aug/23 $$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\mathrm{2}+{x}} \…

Question Number 196396 by mathlove last updated on 24/Aug/23 $$\underset{n\to \mathrm{\infty }}{\lim }[{(-1)}^n\cdot n]=?$$ Commented by mokys last updated on 24/Aug/23 $$\mathrm{\infty }$$ Terms…

Question Number 196135 by cortano12 last updated on 18/Aug/23 Terms of Service Privacy Policy Contact: info@tinkutara.com