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Category: Relation and Functions

let-f-x-arctan-2x-1-x-1-calculate-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-

Question Number 81431 by abdomathmax last updated on 13/Feb/20 $${let}\:{f}\left({x}\right)=\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{x}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Commented by abdomathmax last updated on 20/Feb/20…

g-x-cos-2arcsinx-calculate-dg-dx-and-d-2-g-dx-2-2-find-1-2-1-2-g-x-dx-

Question Number 146901 by mathmax by abdo last updated on 16/Jul/21 $$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{cos}\left(\mathrm{2arcsinx}\right)\:\: \\ $$$$\mathrm{calculate}\:\frac{\mathrm{dg}}{\mathrm{dx}}\:\mathrm{and}\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{g}}{\mathrm{dx}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\mathrm{find}\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by ArielVyny…

let-and-roots-of-z-2-3z-5-0-simlify-U-n-k-0-n-k-k-and-V-n-k-0-n-1-k-1-k-

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

find-lim-x-0-sin-tan-2x-x-1-cos-pix-2-x-2-

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

calculate-lim-x-0-tan-2x-2tanx-2tan-3-x-x-5-

Question Number 81027 by abdomathmax last updated on 09/Feb/20 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{tan}\left(\mathrm{2}{x}\right)−\mathrm{2}{tanx}−\mathrm{2}{tan}^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} } \\ $$ Commented by john santu last updated on 09/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{tan2}{x}\:}{\mathrm{2}{x}}.\left(\mathrm{2}{x}\right)−\frac{\mathrm{2tan}\:{x}}{{x}}.\left({x}\right)−\frac{\mathrm{2tan}^{\mathrm{3}}…