Limit your limits!

Calculus Level 5

\[ A=\lim_{x\rightarrow 0} (1+\text{arctan}(\text{arcsin}(x))+\text{arctan}(\text{arcsin}(2x))+\cdots+\text{arctan}(\text{arcsin}(nx)))^{\frac{1}{\text{arcsin}(nx)}}\]

What is the value of \(\lfloor A \rfloor \) when \(n=10\)?

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