Evaluate ​ lim x→0 f(x), where f(x) = {(|x|/x, x≠0) (0, x =0) [x∈ 0]

Question

Evaluate

\(\lim\limits _{x \to 0}\) f(x), where  \(f(x) = \begin{cases} \frac{|x|}{x} & x\neq0\\ 0, & x =0 \end{cases}\)

Answer 1

\(\lim\limits _{x \to 0^-}\) f(x) = \(\lim\limits _{x \to 0}\) -1 = -1

\(\lim\limits _{x \to 0^+}\) f(x) = \(\lim\limits _{x \to 0}\) 1 = 1

Therefore; \(\lim\limits _{x \to 0^-}\) f(x) \(\neq\)\(\lim\limits _{x \to 0^+}\)f(x)

Hence \(\lim\limits _{x \to 0}\) f(x)  does not exist