Engineering Board Exam Reviewer · One-Sided Limits and Continuity · medium

Determine whether x 2|x-2|/x-2 exists.

1. Does not exist
2. 1
3. -1
4. 0

Answer

A. Does not exist

Solution

For x<2, |x-2|/x-2=2-x/x-2=-1; for x>2, it equals 1. Since the one-sided limits differ, the limit does not exist.

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