Category: Relation and Functions

Question Number 143860 by mathmax by abdo last updated on 19/Jun/21 $$\mathrm{calculate}{\int }_0^{\mathrm{\infty }}\mathrm{x}{\mathrm{e}}^{-{\mathrm{x}}^2}\log (1+{\mathrm{e}}^{\mathrm{x}})\mathrm{dx}$$ Answered by mathmax by abdo last…

Question Number 78286 by msup trace by abdo last updated on 15/Jan/20 $$find{A}_n=\int {\int }_{[0,n[}{e}^{-(x^2+3y^2)}sin(x^2+3y^2)dxdy$$$$and{lim}_{n\to +\mathrm{\infty }}{A}_n$$$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma{n}\:{A}_{{n}}…

Question Number 78261 by msup trace by abdo last updated on 15/Jan/20 $$let{U}_n={\int }_0^1\frac{x^n}{1+x}dxcalculate$$$$U_n+U_{n+1}$$ Commented by jagoll…

Question Number 143730 by mathmax by abdo last updated on 17/Jun/21 $$\mathrm{find}{\lim }_{\mathrm{x}\to 0}\frac{\sin \left(\sin (1-\mathrm{cosx})\right)-1+\cos (\mathrm{x}-\mathrm{sinx})}{{\mathrm{x}}^3}$$ Answered by TheHoneyCat last updated on 17/Jun/21 $$\mathrm{sin}{x}={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}+{o}\left({x}^{\mathrm{4}}…

Question Number 78136 by msup trace by abdo last updated on 14/Jan/20 $$givetheequationoftangente$$$$atp(x_0,f\left(x_0\right))$$$$1)f\left(x\right)=e^{-x^2}ln(1-2x)x_0=-1$$$$\left.\mathrm{2}\right){f}\left({x}\right)=\left({x}^{\mathrm{2}} −\mathrm{3}\right){arctan}\left({x}^{\mathrm{2}}…