Let Lim x tends to C+ f(X) exists and are finite. and lim x tends to c- f(x) . Show that I an open interval be a monotone function, and assume f is discontinuous at f: I R Solution since it is monotonic function the limit exists at all points except at discontinuity Reduce the problem to the case of proving for increasing functions by observing that if f is decreasing, ?f is increasing. Show that the one sided limits exists and are given by: limt?c+ f(t)=inf{f(x)?x>c} and limt?c?f(t)=sup{f(x)?x.