Category: Relation and Functions

Question Number 81431 by abdomathmax last updated on 13/Feb/20 $$letf\left(x\right)=\frac{arctan\left(2x\right)}{1+x}$$$$1)calculate{f}^{\left(n\right)}\left(x\right)and{f}^{\left(n\right)}\left(0\right)$$$$2)developpfatintegrserie$$ Commented by abdomathmax last updated on 20/Feb/20…

Question Number 81428 by abdomathmax last updated on 13/Feb/20 $$calculate{lim}_{x\to +\mathrm{\infty }}{x}^{3}ln(1+e^{-x^2})$$ Answered by mind is power last updated on 13/Feb/20…

Question Number 146902 by mathmax by abdo last updated on 16/Jul/21 $$\mathrm{let}\alpha \mathrm{and}\beta \mathrm{roots}\mathrm{of}{\mathrm{z}}^2+3\mathrm{z}+5=0$$$$\mathrm{simlify}{\mathrm{U}}_{\mathrm{n}}=\sum _{\mathrm{k}=0}^{\mathrm{n}}({\alpha }^{\mathrm{k}}+{\beta }^{\mathrm{k}})$$$$\mathrm{and}\:\mathrm{V}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\left(\frac{\mathrm{1}}{\alpha^{\mathrm{k}}…

Question Number 146898 by mathmax by abdo last updated on 16/Jul/21 $$\mathrm{calculate}{\int }_0^{\mathrm{\infty }}\frac{\mathrm{cosx}}{({\mathrm{x}}^2+1)({\mathrm{x}}^2+2)({\mathrm{x}}^2+3)}\mathrm{dx}$$ Answered by qaz last updated on…

Question Number 146705 by mathmax by abdo last updated on 15/Jul/21 $$\mathrm{find}{\lim }_{\mathrm{x}\to 0}\frac{\sin (\tan \left(2\mathrm{x}\right)-\mathrm{x})+1-\cos \left(\pi {\mathrm{x}}^2\right)}{{\mathrm{x}}^2}$$ Answered by Olaf_Thorendsen last updated on 15/Jul/21 $${f}\left({x}\right)\:=\:\frac{\mathrm{sin}\left(\mathrm{tan}\left(\mathrm{2}{x}\right)−{x}\right)+\mathrm{1}−\mathrm{cos}\left(\pi{x}\right)}{{x}^{\mathrm{2}}…