Category: Relation and Functions

Question Number 106134 by mathmax by abdo last updated on 03/Aug/20 $$\mathrm{let}\mathrm{g}\left(\mathrm{x}\right)=\mathrm{arcatan}(1+\mathrm{x})\ln (1-2\mathrm{x})$$$$1)\mathrm{find}{\mathrm{g}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)\mathrm{and}{\mathrm{g}}^{\left(\mathrm{n}\right)}\left(0\right)$$$$2)\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{integr}\mathrm{serie}$$$$3/\mathrm{calculate}{\int }_{-\frac{1}{4}}^{\frac{1}{4}}\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx}$$ Terms…

Question Number 171484 by infinityaction last updated on 16/Jun/22 $$$$$$letf\left(x\right)=x+\frac{2}{1.3}{x}^3+\frac{2.4}{1.3.5}{x}^5+\frac{2.4.6}{1.3.5.7}{x}^7+\dots \dots \dots$$$$\mathrm{\forall }x\in (0,1)thevalueoff\left(\frac{1}{\sqrt{2}}\right)=?$$ Commented by mr W last updated…

Question Number 40370 by math khazana by abdo last updated on 20/Jul/18 $$let{u}_n=\sum _{k=0}^n(3k+1){(-1)}^k$$$$1)calculateintermsofn$$$${S}_{{n}} ={u}_{\mathrm{0}} \:+{u}_{\mathrm{1}} +{u}_{\mathrm{2}} +….+{u}_{{n}} \…

Question Number 105843 by bobhans last updated on 01/Aug/20 $${\left(3x\right)}^{1+\log {}_3\left(3x\right)}>81x^2$$$$findthesolutionset$$ Answered by bemath last updated on 01/Aug/20 $$\left(\mathrm{3}{x}\right)^{\mathrm{1}+\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{3}{x}\right)}…

Question Number 105735 by bobhans last updated on 31/Jul/20 $$Whatisthecubicpolynomialfory\left(0\right)=1;$$$$y\left(1\right)=0;y\left(2\right)=1andy\left(3\right)=10$$ Commented by PRITHWISH SEN 2 last updated on 31/Jul/20 $$\mathrm{y}\left(\mathrm{x}\right)=\:\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}−\mathrm{1}\right)…