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

(a) \(f\left( x \right)=\frac{1}{{{x}^{2}}-4}\)

(b) \(f\left( x \right)=\frac{1}{\sqrt{x+2}}\)

(c) \(f\left( x \right)=\tan x\)

(d) \(f\left( x \right)=\frac{\sin x}{x}\)

(e) \(f\left( x \right)=\left\{ \begin{aligned} & x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|x|\ge 1 \\ & {{x}^{2}}\,\,\,\,\,\,\,\,\,\,\,\,\,|x|>1 \\ \end{aligned} \right.\)

(f) \(f\left( x \right)=\frac{{{x}^{2}}-4}{x+2}\)

(g) \(f\left( x \right)=\frac{x}{{{x}^{3}}+27}\)

(h) \(f\left( x \right)=\sqrt{{{x}^{2}}-9}\)

(i) \(f\left( x \right)=\left\{ \begin{aligned} & x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|x|\ge \frac{\pi }{2} \\ & \sin x\,\,\,\,\,\,\,\,\,\,\,\,\,\,|x|<\frac{\pi }{2} \\ \end{aligned} \right.\)

(j) \(f\left( x \right)=\ln x\)

(k) \(f\left( x \right)={{e}^{-x}}\)

(l) \(f\left( x \right)=\left[ x \right]\)

(m) \(f\left( x \right)=\left[ x \right]+x\)