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Originally Posted by MageB420666
Use L'Hospital's rule.
in this case f(x) = |x-c| and g(x) = x-c, so f'(x) = 1 and g'(x) = 1, so according to L'Hospital's rule, the limit is 1
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The problem with that is the absolute value thrown in there. Thus, if you approach the limit from the left side, the function is negative 1, but if you approach it from the right side, the function is positive 1. For that reason, L'Hospital's rule is wrong. Good rule though.