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Question Number 67015 by mathmax by abdo last updated on 21/Aug/19
$${let}\:{f}\left({x}\right)\:={arctan}\left(\mathrm{1}+{e}^{−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \right) \\ $$$${calculate}\:{f}^{'} \left({x}\right)\:\:{and}\:{f}^{''} \left({x}\right). \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow−\infty} \:\:\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{variation}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{4}\right){give}\:{the}\:{equation}\:{of}\:{tangent}\:{to}\:{C}_{{f}} \:{at}\:\:{A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right) \\ $$