Question
Download Solution PDFWhich one of the following is correct regarding \(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3}\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
\(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3}\)
LHL = \(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3} = \frac{-(x-3)}{x-3} = -1\)
RHL = \(\rm \lim_{x\rightarrow 3}\frac{|x-3|}{x-3} = \frac{(x-3)}{x-3} =1\)
LHL ≠ RHL; limit does not exist
∴ Option (d) is correct.
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