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Category: Relation and Functions

What-is-the-nearest-point-in-f-x-to-5-2-where-f-x-0-5x-2-3-

Question Number 192132 by Red1ight last updated on 09/May/23 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{point}\:\mathrm{in}\:{f}\left({x}\right)\:\mathrm{to}\:\left(\mathrm{5},\mathrm{2}\right) \\ $$$$\mathrm{where}\:{f}\left({x}\right)=−\mathrm{0}.\mathrm{5}{x}^{\mathrm{2}} +\mathrm{3} \\ $$ Answered by mehdee42 last updated on 09/May/23 $${according}\:{to}\:{the}\:{diagram}: \\ $$$${let}\::{H}\left({h},{f}\left({h}\right)\right)\:\:…

let-f-x-1-x-2-1-let-U-n-f-n-x-prove-that-k-0-n-C-n-k-U-k-U-n-1-k-0-for-n-2-2-developp-f-at-integr-serie-

Question Number 60706 by maxmathsup by imad last updated on 24/May/19 $${let}\:{f}\left({x}\right)\:=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{let}\:{U}_{{n}} ={f}^{\left({n}\right)} \left({x}\right)\:\:{prove}\:{that}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{U}_{{k}} {U}_{{n}+\mathrm{1}−{k}} =\mathrm{0}\:\:{for}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:.…