Let f"(x) be continuous at x = 0. If limx→02fx-3a f2x+bf8xsin2x exists and f0≠0, f'0≠0, then the value of 3ab  is _____

We  have            L=limx→0 2fx-3af2x+bf8xsin2xFor  the  limit  to  exist,   we  have             2f0-3af0+bf0=0or      3a-b=2           f0≠0,    given                      1or      L=limx→02f'x-6a  f'2x+8b f'8x2xFor   the   limit  to  exist,  we  have         2f'0-6af'0+8bf'0=0⇒   3a-4b=1          f'0≠0,   given                         2Solving   equations  1  and   2,   we   have   a=79   and   b=13.