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Category: Relation and Functions

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Question Number 40116 by maxmathsup by imad last updated on 15/Jul/18 $${let}\:{f}\left({x}\right)\:=\:\frac{{e}^{{x}^{\mathrm{2}} } −\mathrm{1}}{{x}}\:\:{if}\:{x}\neq\mathrm{0}\:\:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${prove}\:{that}\:\:{f}^{−\mathrm{1}} \left({x}\right)={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{2}}\:+{o}\left({x}^{\mathrm{3}} \right)\:\:\:\left({x}\rightarrow\mathrm{0}\right) \\ $$ Terms of Service Privacy…

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Question Number 40107 by maxmathsup by imad last updated on 15/Jul/18 $${prove}\:{the}\:{relations} \\ $$$$\left.\mathrm{1}\left.\right)\left.\:\forall{t}\:\in\right]\mathrm{0},\mathrm{1}\right]\:\:\:{arctan}\left(\frac{\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{{t}}\right)={arccost} \\ $$$$\left.\mathrm{2}\right)\:\forall\:{t}\in\left[−\mathrm{1},\mathrm{1}\right]\:\:\:\:\mathrm{2}\:{arccos}\sqrt{\frac{\mathrm{1}+{t}}{\mathrm{2}}}\:={arccost} \\ $$ Answered by math khazana by abdo…