Category: Relation and Functions

Question Number 31531 by abdo imad last updated on 09/Mar/18 $$letgivef\left(x\right)=\frac{1}{x}+\sum _{n=1}^{\mathrm{\infty }}(\frac{1}{x+n}+\frac{1}{x-n})withx\in R-Z$$$$1)provetheexistenceoff\left(x\right)$$$$2)provethatfis1-periodic$$$$3)provethatf\left(\frac{x}{2}\right)+f\left(\frac{x+1}{2}\right)=2f\left(x\right).$$ Terms of Service Privacy…

Question Number 31526 by abdo imad last updated on 09/Mar/18 $$1)find{lim}_{n\to \mathrm{\infty }}{\left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)}^n$$$$2)let0<\theta <\frac{\pi }{2}calculate{lim}_{n\to \mathrm{\infty }}\frac{1}{2^n}{\left({}^n\sqrt{cos\theta }{+}^n\sqrt{sin\theta }\right)}^n$$ Commented by abdo…

Question Number 31521 by abdo imad last updated on 09/Mar/18 $$studytheconvergenceof{u}_n=\sqrt{n+1}-\sqrt{n-1}$$ Commented by abdo imad last updated on 12/Mar/18 $${we}\:{have}\:{u}_{{n}} =\sqrt{{n}}\left(\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{n}}}\:−\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{n}}}\:\right)\:{but} \…

Question Number 31510 by abdo imad last updated on 09/Mar/18 $$find{lim}_{n\to \mathrm{\infty }}{}^n\sqrt{\prod _{k=1}^n(1+\frac{k}{n^2}})$$ Commented by abdo imad last updated on…

Question Number 31500 by abdo imad last updated on 09/Mar/18 $$let{L}_n\left(x\right)=e^x{\left(e^{-x}{x}^n\right)}^{\left(n\right)}$$$$1)provethat{L}_{n}isapolynomial$$$$2)find{degL}_{n}andtheleadingcoefficient.$$ Commented…