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Category: Relation and Functions

let-f-x-arctan-x-2-3-1-calculate-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-3-calculate-0-1-f-x-dx-

Question Number 97622 by mathmax by abdo last updated on 08/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{arctan}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{3}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$…

let-u-n-0-1-x-n-sin-pix-dx-1-prove-that-u-n-converges-2-prove-that-u-n-0-pi-sint-t-dt-

Question Number 32042 by abdo imad last updated on 18/Mar/18 $${let}\:{u}_{{n}} \:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{x}^{{n}} \:{sin}\left(\pi{x}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\Sigma\:{u}_{{n}} \:{converges} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\Sigma\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sint}}{{t}}{dt}\:. \\ $$…

let-consider-the-sequence-u-n-u-0-0-1-and-n-N-u-n-1-u-n-u-n-2-1-give-a-simple-equivalent-of-u-n-2-find-the-nature-of-u-n-

Question Number 32033 by abdo imad last updated on 18/Mar/18 $${let}\:{consider}\:{the}\:{sequence}\:\:\left({u}_{{n}} \right)\:\:/{u}_{\mathrm{0}} \in\left[\mathrm{0},\mathrm{1}\right]\:{and} \\ $$$$\forall{n}\in{N}\:\:{u}_{{n}+\mathrm{1}} =\:{u}_{{n}} \:−{u}_{{n}} ^{\mathrm{2}} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{a}\:{simple}\:{equivalent}\:{of}\:\:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} . \\ $$…