Category: Relation and Functions

Question Number 30412 by abdo imad last updated on 22/Feb/18 $$fisafunctionincreazing\left(ordecreazing\right)on]0,1]$$$$provethat{lim}_{n\to \mathrm{\infty }}\frac{1}{n}\sum _{q=1}^{n}f\left(\frac{q}{n}\right)={\int }_0^{1}f\left(t\right)dt.$$$$$$ Terms of Service…

Question Number 95941 by mathmax by abdo last updated on 28/May/20 $$\mathrm{prove}\mathrm{that}\frac{1}{\mathrm{sinx}}=\sum _{\mathrm{n}=-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{{(-1)}^{\mathrm{n}}}{\mathrm{x}+\mathrm{n}\pi }$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 161387 by savitar last updated on 17/Dec/21 $$sin\sqrt{1+{\pi }^2{n}^2}\sim \frac{{(-1)}^n}{2\pi n}?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 95839 by mathmax by abdo last updated on 28/May/20 $$\mathrm{solve}{\mathrm{y}}^{\left(3\right)}-{2\mathrm{y}}^{\left(2\right)}+3\mathrm{y}-2\mathrm{y}=\mathrm{sinx}$$ Commented by john santu last updated on 28/May/20 $$\mathrm{homogenous}\:\mathrm{solution}…

Question Number 95837 by mathmax by abdo last updated on 28/May/20 $$\mathrm{let}\mathrm{p}\left(\mathrm{x}\right)={(1+\mathrm{ix}+{\mathrm{x}}^2)}^{\mathrm{n}}-{(1-\mathrm{ix}+{\mathrm{x}}^2)}^{\mathrm{n}}$$$$1)\mathrm{determine}\mathrm{roots}\mathrm{of}\mathrm{p}\left(\mathrm{x}\right)$$$$2)\mathrm{find}\mathrm{p}\left(\mathrm{x}\right)\mathrm{at}\mathrm{form}\mathrm{\Sigma }{\mathrm{a}}_{\mathrm{i}}{\mathrm{x}}^{\mathrm{i}}$$$$3)\mathrm{ddtermne}\mathrm{p}\left(\mathrm{x}\right)\mathrm{at}\mathrm{form}\arctan$$$$\left.\mathrm{4}\right)\:\mathrm{factorize}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \…