Consider a function \(f : \mathbb{R} \rightarrow \mathbb{R}\) such that

\[f(x) = \begin{cases} \sin(\pi x) & \text{if } x \in \mathbb{Q} \\ \tan(\pi \sqrt{|x|}) & \text{if }x \not \in \mathbb{Q}\end{cases}\]

Find the sum of all positive integers \(N < 100\), such that \(\displaystyle\lim _{x \rightarrow N} f(x) \) exists.

This problem is part of the set - Piecewise-defined Functions

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