Limit of |x|/x as x approaches 0 Does Not Exist | Calculus 1
We show the limit of absolute value of x over x, as x goes to zero, does not exist. This is because as x approaches 0 from the left, it is negative, so |x| = -x, and then |x|/x = -x/x = -1. However, as x approaches 0 from the right, it is positive, so |x|/x = x/x = 1. Thus, the one sided limits are different and so the two sided limit does not exist. #Calculus1
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