let-f-x-arctan-1-e-1-x-2-calculate-f-x-and-f-x-1-find-lim-x-f-x-and-lim-x-f-x-3-study-the-variation-of-f-x-4-give-the-equation-of-tangent-to-C-f-at-A-1-f-1-

Tinku Tara June 3, 2023 Relation and Functions 0 Comments

Question Number 67015 by mathmax by abdo last updated on 21/Aug/19

let f(x) =arctan(1+e^(−(√(1+x^2 ))) ) calculate f^′ (x) and f^(′′) (x). 1)find lim_(x→+∞) f(x) and lim_(x→−∞) f(x) 3)study the variation of f(x) 4)give the equation of tangent to C_f at A(1,f(1))

$${let}\:{f}\left({x}\right)\:={arctan}\left(\mathrm{1}+{e}^{−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \right) \\ $$$${calculate}\:{f}^{'} \left({x}\right)\:\:{and}\:{f}^{''} \left({x}\right). \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow−\infty} \:\:\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{variation}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{4}\right){give}\:{the}\:{equation}\:{of}\:{tangent}\:{to}\:{C}_{{f}} \:{at}\:\:{A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right) \\ $$

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let-f-x-arctan-1-e-1-x-2-calculate-f-x-and-f-x-1-find-lim-x-f-x-and-lim-x-f-x-3-study-the-variation-of-f-x-4-give-the-equation-of-tangent-to-C-f-at-A-1-f-1-

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