Question: Determine the numbers, if any, at which the given function is discontinuous.

1. \(f\left( x \right)=\frac{1}{{{x}^{2}}-4}\)
2. \(f\left( x \right)=\frac{1}{\sqrt{x+2}}\)
3. \(f\left( x \right)=\tan x\)
4. \(f\left( x \right)=\frac{\sin x}{x}\)
5. \(f\left( x \right)=\left\{ \begin{aligned} & x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|x|\ge 1 \\ & {{x}^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\,|x|>1 \\ \end{aligned} \right.\)
6. \(f\left( x \right)=\frac{{{x}^{2}}-4}{x+2}\)
7. \(f\left( x \right)=\frac{x}{{{x}^{3}}+27}\)
8. \(f\left( x \right)=\sqrt{{{x}^{2}}-9}\)
9. \(f\left( x \right)=\left\{ \begin{aligned} & x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|x|\ge \frac{\pi }{2} \\ & \sin x\,\,\,\,\,\,\,\,\,\,\,\,\,\,|x|<\frac{\pi }{2} \\ \end{aligned} \right.\)
10. \(f\left( x \right)=\ln x\)
11. \(f\left( x \right)={{e}^{-x}}\)
12. \(f\left( x \right)=\left[ x \right]\)
13. \(f\left( x \right)=\left[ x \right]+x\)

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