A function f(x) has removable discontinuity at x=a if limx→ a(f(x)) exists and finite,
but function is either undefined at x=a or limx→ a(f(x))≠ f(a)
f(x) has step discontinuity if one-sided limits exist and finite but not equal.
f(x) has essential discontinuity if one or both of the one-sided limits don't exist or are infinite.