Let x − 4 = n
⟹ As x ⟶ 4,
n ⟶ 0
∴ L.H.S
\(\lim\limits_{n \to 0-}\frac{|n|}{n}\)
= \(\lim\limits_{n \to 0-}\frac{-n}{n}\)
= \(\lim\limits_{n \to 0-}\)(-1)
= -1
R.H.S,
\(\lim\limits_{n \to 0+}\frac{|n|}{n}\)
= \(\lim\limits_{n \to 0+}\frac{-n}{n}\)
= \(\frac{n}{n}=\lim\limits_{n \to 0+}(1)\)
=1
Since L.H.S ≠ R.H.S
\(\lim\limits_{x \to 4}\frac{|x-4|}{x-4}\) does not exist