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let-f-x-1-x-1-x-2-arctan-xt-2-x-t-dt-calculate-f-x-2-find-lim-x-0-f-x-




Question Number 71301 by turbo msup by abdo last updated on 13/Oct/19
let f(x)=∫_(1+x) ^(1+x^2 )  ((arctan(xt+2))/(x+t))dt  calculate f^′ (x)  2)find lim_(x→0) f(x)
$${let}\:{f}\left({x}\right)=\int_{\mathrm{1}+{x}} ^{\mathrm{1}+{x}^{\mathrm{2}} } \:\frac{{arctan}\left({xt}+\mathrm{2}\right)}{{x}+{t}}{dt} \\ $$$${calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right) \\ $$

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