Category: Relation and Functions

Question Number 66317 by mathmax by abdo last updated on 12/Aug/19 $$calculate{lim}_{x\to 0}\frac{ln\left(cosx\right)}{1-cos\left(2x\right)}$$ Commented by kaivan.ahmadi last updated on 12/Aug/19 $$\equiv{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left({cosx}\right)}{\mathrm{2}{x}^{\mathrm{2}} }\overset{{hop}}…

Question Number 680 by 123456 last updated on 23/Feb/15 $$findallf:\mathbb{N}\to \mathbb{N}suchthat$$$$f[n+f\left(n\right)]=2f\left(n\right)$$ Answered by prakash jain last updated on 23/Feb/15 $$f\left(n\right)=kn+k_1$$$${f}\left({n}+{kn}+{k}_{\mathrm{1}}…

Question Number 655 by 123456 last updated on 19/Feb/15 $$f\left(z\right)=\frac{1-\frac{1-z^2}{2+z^2}}{2+\frac{1-z^2}{2+z^2}}$$$$\frac{f\left(0\right)+f\left(1\right)}{2}-f\left(\frac{1}{2}\right)=?$$ Answered by prakash jain last updated on…

Question Number 66171 by mathmax by abdo last updated on 10/Aug/19 $$find{lim}_{n\to +\mathrm{\infty }}\frac{1}{n^2}\{sin\left(\frac{1}{n^2}\right)+2sin\left(\frac{4}{n^2}\right)+\dots .(n-1)sin\left(\frac{{(n-1)}^2}{n^2}\right)\}$$ Commented by mathmax by abdo…

Question Number 131641 by liberty last updated on 07/Feb/21 $$\mathrm{What}\mathrm{is}\mathrm{f}\left(\mathrm{x}\right)\mathrm{if}:2\mathrm{f}\left(\mathrm{x}\right)-\mathrm{x}\mathrm{f}\left(\frac{2\mathrm{x}+3}{\mathrm{x}-2}\right)=3$$$$\mathrm{when}\mathrm{x}\ne 2?$$ Answered by EDWIN88 last updated on 07/Feb/21 $$\left(1\right)2\mathrm{f}\left(\mathrm{x}\right)-\mathrm{x}\mathrm{f}\left(\frac{2\mathrm{x}+3}{\mathrm{x}-2}\right)=3$$$$\:\mathrm{replacing}\:\mathrm{x}\:\mathrm{by}\:\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{x}−\mathrm{2}} \…