Confused with this limit?
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Confused with this limit?

[From: ] [author: ] [Date: 14-03-09] [Hit: ]
......
is it 0/0 ? or infinity or undefined??

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When x < 0, then |x| = −x
lim[x→0⁻] |x|/x = lim[x→0⁻] −x/x = lim[x→0⁻] −1 = −1

When x > 0, then |x| = x
lim[x→0⁺] |x|/x = lim[x→0⁺] x/x = lim[x→0⁺] 1 = 1

Since left-sided limit and right-sided limits are not equal,
then lim[x→0] |x|/x does not exist

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It doesn't exist since it approaches -1 from the left and 1 from the right
1
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