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Dear student,

\lim_{x \to 2} \frac{|x - 2|}{x - 2} RHL : \lim_{x \to 2^{+}} \frac{|x - 2|}{x - 2} = \lim_{h \to 0} \frac{|2 + h - 2|}{2 + h - 2} = \lim_{h \to 0} \frac{|h|}{h} = 1 LHL : \lim_{x \to 2^{-}} \frac{|x - 2|}{x - 2} = \lim_{h \to 0} \frac{|2 - h - 2|}{2 - h - 2} = \lim_{h \to 0} \frac{|- h|}{- h} = \lim_{h \to 0} \frac{h}{- h} = - 1 Since, LHL \neq RHL, so at x = 2 limit does not exist .

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