Prove f(x) is discontinuous at 0 for the function f(x) = x if x>=0 and f(x) = 1 - x if x < 0 using the epsilon-delta method.

Answer 1

since the limit on the left is 0 and on the right it is 1,

There is clearly no L such that

limit(delta->0) |f(x)-epsilon| < 0 if |x-0| <= delta