A calculus problem by Akshat Sharda

Calculus Level 4

limx0sin1xtan1xln(1+x3)=A\lim_{x\rightarrow 0} \dfrac{\sin^{-1} x -\tan^{-1} x}{\ln (1+x^{3} )} = A

Find the value of 1A\dfrac{1}{A}.

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