Category: Relation and Functions

Question Number 38367 by Zuarkton last updated on 24/Jun/18 $$Iff\left(x\right)=x^3+1then{f}^{-1}\left(x\right)=?$$ Commented by rahul 19 last updated on 24/Jun/18 $${(x-1)}^{\frac{1}{3}}$$…

Question Number 103763 by mathmax by abdo last updated on 17/Jul/20 $$\mathrm{calculate}\left\{\sum _{\mathrm{n}=0}^{\mathrm{\infty }}{(-1)}^{\mathrm{n}}{\mathrm{x}}^{\mathrm{n}}\right\}\times \left\{\sum _{\mathrm{n}=\mathrm{o}}^{\mathrm{\infty }}\frac{{\mathrm{x}}^{2\mathrm{n}}}{\mathrm{n}+1}\right\}$$ Answered by mathmax by…

Question Number 38195 by maxmathsup by imad last updated on 22/Jun/18 $$letx⩾1and\delta \left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{n^x}$$$$1)calculate\delta \left(x\right)intermsof\xi \left(x\right)ifx>1$$$$2)find\delta \left(1\right)$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }…

Question Number 38112 by maxmathsup by imad last updated on 21/Jun/18 $$provethatarctan\left(x\right)=\frac{i}{2}ln\left(\frac{i+x}{i-x}\right)for\mid x\mid <1$$ Commented by prof Abdo imad last updated on 24/Jun/18 $${we}\:{have}\:{i}+{x}={x}+{i}=\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\left(\:\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}}…

Question Number 38108 by maxmathsup by imad last updated on 21/Jun/18 $$find\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{n^2}$$ Commented by prof Abdo imad last updated…