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let-A-2-arctan-1-t-pi-4-2-t-2-t-dt-find-lim-0-A-




Question Number 57948 by maxmathsup by imad last updated on 14/Apr/19
let A(ξ) =∫_ξ ^ξ^2      ((arctan(1+ξt)−(π/4))/( (√(2+ξt))−(√(2−ξt)))) dt  find lim_(ξ →0)   A(ξ) .
$${let}\:{A}\left(\xi\right)\:=\int_{\xi} ^{\xi^{\mathrm{2}} } \:\:\:\:\frac{{arctan}\left(\mathrm{1}+\xi{t}\right)−\frac{\pi}{\mathrm{4}}}{\:\sqrt{\mathrm{2}+\xi{t}}−\sqrt{\mathrm{2}−\xi{t}}}\:{dt} \\ $$$${find}\:{lim}_{\xi\:\rightarrow\mathrm{0}} \:\:{A}\left(\xi\right)\:. \\ $$$$ \\ $$

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