# Piecewise Functions - 5

Calculus Level 4

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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