Category: Relation and Functions

Question Number 39702 by math khazana by abdo last updated on 10/Jul/18 $$letf\left(x\right)=2\sqrt{x-\sqrt{x-3}+2}$$$$1)find{D}_f$$$$2)calculate{f}^{{}^{\prime }}\left(x\right)$$$$3)determine{f}^{-1}\left(x\right)$$$$\left.\mathrm{4}\right)\:{calculate}\:\left({f}^{−\mathrm{1}} \right)^{'} \left({x}\right)…

Question Number 39695 by maxmathsup by imad last updated on 09/Jul/18 $$letf\left(x\right)=ln(2xarctan\sqrt{2x^2-1)}$$$$1)find{D}_f$$$$2)calculate{f}^{{}^{\prime }}\left(x\right)anddetermineitssign.$$$$3)determinetheequationofassymptoteatpontA(1,f\left(1\right))$$$$3)findaandbfromR/f\left(x\right)\sim a(x-1)+b(x\to 1)$$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 39632 by abdo mathsup 649 cc last updated on 08/Jul/18 $$let{S}_n=\sum _{k=1}^n\frac{1}{k\sqrt{k}}$$$$findaequivalentof{S}_n(n\to +\mathrm{\infty })$$ Terms of Service Privacy…

Question Number 39519 by math khazana by abdo last updated on 07/Jul/18 $$simplify$$$$1)A_n=\frac{1}{\sqrt{a}}\{{\left(\frac{1+\sqrt{a}}{2}\right)}^n-{\left(\frac{1-\sqrt{a}}{2}\right)}^n\}withnnatural$$$$integranda>0$$$$\left.\mathrm{2}\right)\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}{x}+\mathrm{1}}}\left\{\:\left(\frac{\mathrm{1}+\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\mathrm{2}}\right)^{{n}} \:−\left(\frac{\mathrm{1}−\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\mathrm{2}}\right)^{{n}} \right\} \…

Question Number 39517 by math khazana by abdo last updated on 07/Jul/18 $$findradiusofS\left(x\right)=\sum _{n=1}^{\mathrm{\infty }}\frac{x^n}{n^2}$$$$andcalculateitssum$$$$\left.\mathrm{2}\right)\:{find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:\:{and}\:\:\sum_{{n}=\mathrm{1}} ^{\infty}…