1.3 Limits that Fail to Exist [01] - |x|/x

http://www.rootmath.org
http://www.rootmath.org/calculus/limits-that-fail-to-exist

Some limits don't exist. The absolute value of x over x, |x|/x, has no limit as x approaches 0. This is because there is a jump in the graph at zero, or a jump discontinuity. This causes the value of the function to differ at the two sides of the jump and so the limit fails to exist.