The constant difference theorem states that iff (x)=g'(x) for all x on an interval, then f(x)=g (x)+k, for some real constant k. (0) show that if f(x)=g'(x) for all real x, and if fla)=g(a) for some real a, then f(x) for all real x. (ii) confirm the trigonometric identity sin'(x)+cos? (x) = 1, using the result from (i), treating the lhs as flx) and the rhs as g(x). (b) determine the continuity of the function below, giving any points where it is discontinuous. are these removable or non-removable points of discontinuity? explain carefully, using one sided limits, how you know that these points are either removable or non-removable discontinuities. x2-100 f(x)x10