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Category: Relation and Functions

let-u-0-4-and-u-n-1-2u-n-3-1-calculate-u-n-interms-of-u-0-and-n-2-study-the-convergence-of-u-n-

Question Number 40124 by maxmathsup by imad last updated on 15/Jul/18 $${let}\:{u}_{\mathrm{0}} \geqslant\mathrm{4}\:\:{and}\:\:{u}_{{n}+\mathrm{1}} =\mathrm{2}{u}_{{n}} −\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{u}_{{n}} \:{interms}\:{of}\:{u}_{\mathrm{0}} \:{and}\:{n} \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{convergence}\:{of}\:\left({u}^{{n}} \right) \\ $$ Terms…

let-f-x-e-x-2-1-x-if-x-0-and-f-0-0-prove-that-f-1-x-x-x-3-2-o-x-3-x-0-

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…

prove-the-relations-1-t-0-1-arctan-1-t-2-t-arccost-2-t-1-1-2-arccos-1-t-2-arccost-

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…