Category: Relation and Functions

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…

Question Number 103458 by bobhans last updated on 15/Jul/20 $$\left(1\right)Ifpandqaretherootsquadratic$$$$equation{x}^2-x-4050=0,findthevalue$$$$of{p}^2+q?$$$$\left(2\right)iff\left(x\right)=\frac{7x+q}{2}andg\left(x\right)=7x+8;$$$$\left(fog\right)\left(4\right)=24.findthevalueofq$$ Answered by bemath…

Question Number 37901 by math khazana by abdo last updated on 19/Jun/18 $$letf\left(x\right)={(1+e^{-x})}^n$$$$1)calculate{f}^{\left(p\right)}\left(x\right)and{f}^{\left(p\right)}\left(o\right)$$$$2)calculate{f}^{\left(n\right)}\left(0\right)$$$$3)developpfatintegrserie.$$…