let-give-f-x-e-1-x-with-f-0-0-1-is-f-derivable-in-point-0-2-prove-that-f-n-F-n-x-e-1-x-with-F-n-is-rational-function-3-calculate-f-6-x-and-f-9-x-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 27784 by abdo imad last updated on 14/Jan/18

let give f(x) = e^(−(1/x)) with f(0)=0 1) is f derivable in point 0? 2)prove that f^((n)) = F_n (x) e^(−(1/x)) with F_(n ) is rational function 3) calculate f^((6)) (x) and f^((9)) (x) .

$${let}\:{give}\:\:{f}\left({x}\right)\:=\:{e}^{−\frac{\mathrm{1}}{{x}}} \:\:\:{with}\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{is}\:{f}\:{derivable}\:{in}\:{point}\:\mathrm{0}? \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:\:{f}^{\left({n}\right)} =\:{F}_{{n}} \left({x}\right)\:{e}^{−\frac{\mathrm{1}}{{x}}} \:\:{with}\:{F}_{{n}\:} {is}\:{rational}\:{function} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\:{f}^{\left(\mathrm{6}\right)} \:\left({x}\right)\:{and}\:\:{f}^{\left(\mathrm{9}\right)} \left({x}\right)\:\:. \\ $$

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let-give-f-x-e-1-x-with-f-0-0-1-is-f-derivable-in-point-0-2-prove-that-f-n-F-n-x-e-1-x-with-F-n-is-rational-function-3-calculate-f-6-x-and-f-9-x-

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