If a function f(x) is defined in x ϵ [a, b], then f(x) is continuous at a if
limx→a+f(x)=f(a)
For a function f(x) defined in [a, b]. the condition for continuity is that the RHL at a should be = f(a), since there are no value for f(x) for x< a. for the same reason we cant take the left hand limit of the function at x = a.