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Question Number 153449 by liberty last updated on 07/Sep/21

 lim_(x→0) ((((1+tan^(−1) (3x)))^(1/3) −((1−sin^(−1) (3x)))^(1/3) )/( (√(1−sin^(−1) (2x)))−(√(1+tan^(−1) (2x))))) =?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{3}{x}\right)}−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{3}{x}\right)}}{\:\sqrt{\mathrm{1}−\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)}−\sqrt{\mathrm{1}+\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)}}\:=? \\ $$

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