Theorem 1 . Let k > I and MY > O be given such that land S_ and Ibn| { _ for each n 2 1 . Then the function f ( *) defined by the Fourier Series f ( * ) = > an cosna + by sinna , - I S IST ! 12 = ] is continuous . Theorem 2. Let k > 2 and M > O be given such that land {`` TE and 1bal { _ for each ~ > 1 . Then the function f ( a) defined by the Fourier Series f ( 20 ) => an cosnat by sinna , - I S IST . 12 = ] is differentiable , and it's derivative is continuous . 1 . ( 20 pt ) Assume Theorem I holds . Give a proof of Theorem 2 2. ( 10 pt ) State a theorem similar to Theorem I and Theorem ? in the case & > 3 . You need not prove it . 3. ( 20 pt ) Last time you computed the Fourier Sine Series of the odd extension of the function f ( *^ ) = et . O