试题答案及评分标准 (2分) (2分) (1分) =(≌+1 (2分) (2分) 0,1,2,3, (1分) (2分) yn(a)=sinn,cosnr (2分) 0,1,2,3, (1分) A=l(+1 (2分) (x)=P(x) (2分) l=0,1,2,3, (1分)☞✌✩✪✫✬✭✮✯ ✰✱ (20 ✲) (1) λn = nπ l 2 (2 ✲) yn(x) = sin nπ l x (2 ✲) n = 1, 2, 3, · · · (1 ✲) (2) λn =  2n + 1 l π 2 (2 ✲) yn(x) = sin 2n + 1 l πx (2 ✲) n = 0, 1, 2, 3, · · · (1 ✲) (3) λn = n 2 (2 ✲) yn(x) = sin nx, cos nx (2 ✲) n = 0, 1, 2, 3, · · · (1 ✲) (4) λl = l(l + 1) (2 ✲) yl(x) = Pl(x) (2 ✲) l = 0, 1, 2, 3, · · · (1 ✲) 12