Cross your limits 4

Calculus Level 4

\[ \large f(x) = \dfrac{ \arcsin(1 - \{x\}) \cdot \arccos(1 - \{x\}) }{ \sqrt{2 \{x\}} (1 - \{x\}) } \]

Let \(f(x) \) be a function as described above. Compute \( \displaystyle \left( \dfrac{\displaystyle \lim_{x\to0^+} f(x)}{\displaystyle \lim_{x\to0^-} f(x)}\right)^2 \).

Notation: \( \{ \cdot \} \) denotes the fractional part function.

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