Category: Relation and Functions

Question Number 35689 by prof Abdo imad last updated on 22/May/18 $$let{S}_n=\sum _{k=1}^n\frac{k^2}{n^2\sqrt{n^2+k^2}}$$$$find{lim}_{n\to +\mathrm{\infty }}{S}_n$$ Commented…

Question Number 35624 by abdo mathsup 649 cc last updated on 21/May/18 $$let{R}_n=\sum _{k=n+1}^{\mathrm{\infty }}\frac{1}{k!}$$$$findaequivalentof{R}_{n}whenn\to +\mathrm{\infty }$$ Terms of Service Privacy…

Question Number 35614 by abdo mathsup 649 cc last updated on 21/May/18 $$calculate\sum _{n=1}^{\mathrm{\infty }}{(-1)}^{n-1}\frac{x^{2n+1}}{4n^2-1}$$ Terms of Service Privacy Policy…

Question Number 101008 by Rio Michael last updated on 29/Jun/20 $$\mathrm{Given}f\left(x\right)=\{\begin{array}{l}\frac{1}{2}{xe}^{\frac{1}{x}},x\ne 0\\ 0,x=0\end{array}$$$$\mathrm{find}$$$$\left(i\right)\mathrm{Thd}\mathrm{domain}\mathrm{of}f$$$$\left(ii\right)\mathrm{check}\mathrm{the}\mathrm{continuity}\mathrm{of}f\mathrm{at}x=0$$$$\left(iii\right)\mathrm{check}\mathrm{its}\mathrm{differentiability}\mathrm{and}\mathrm{its}\mathrm{sign}$$$$\left({i}\right)\:\mathrm{sketch}\:\mathrm{this}\:\mathrm{curve}\:\mathrm{and}\:\mathrm{find}\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:\mathrm{and}\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:{f}\left({x}\right) \…

Question Number 100951 by bemath last updated on 29/Jun/20 Commented by Rasheed.Sindhi last updated on 29/Jun/20 $$Byjohnsantu(answerof$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$2^x(1+2^{x+1})=(y-1)(y+1)$$$${show}\:{that}\:{the}\:{factors}\:{y}−\mathrm{1}\:{and}\:{y}+\mathrm{1}…