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Question Number 94652 by msup by abdo last updated on 20/May/20

find lim_(ξ→0)    ∫_0 ^1      ((sin(ξx))/((√(1+ξx^2 ))−(√(1−ξx^2 ))))dx

$${find}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{{sin}\left(\xi{x}\right)}{\sqrt{\mathrm{1}+\xi{x}^{\mathrm{2}} }−\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}{dx} \\ $$

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