Which one of the following is correct regarding \lim_{x\rightarrow 3}\frac{|x-3|}{x-3}?
- A. Limit exists and is equal to 1
- B. Limit exists and is equal to 0
- C. Limit exists and is equal to -1
- D. Limit does not exist ✓
Correct Answer: D. Limit does not exist
Explanation
Evaluate the left-hand and right-hand limits. As x \to 3^+, |x-3| = x-3, so the right-hand limit is 1. As x \to 3^-, |x-3| = -(x-3), so the left-hand limit is -1. Since the limits are not equal, the overall limit does <strong>NOT</strong> exist.
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