Unction g. show that g also has an essential discontinuity Mc. 52. (a) Prove that iff is continuous everywhere, then is o verify continuous everywhere. (b) Give an example to show that the continuity of | | does not imply the continuity of (c) Give an couample of a function / such that / is continu ilues of ous nowhere, but If] is continuous everywhere, Suppose the function / has the property that there evigan aphing manber H wach that for all or in the interval lie - poet pi. Prove that / is con- 54. Suppose the function f has the property that for each pair of points I. I in the interval (a, b). Prove that J is continuous on (a, b). 55. Prove that if fleth)- /()