Evaluate limx → 0 f(x), where f(x) = {(|x|/x, x ≠ 0), (0, x = 0)

Question

Evaluate \(\lim\limits_{x \to 0} f(x)\), where \(f(x) = \begin{cases} \frac{|x|}{x}, &x≠0 \\ 0, & x=0 \end{cases}\)

Answer 1

We have,

Hence, \(\lim\limits_{x \to 0} f(x)\) does not exist.