解求6+omez+3池 oo+1)cs(+ =5es(6r+1+2+3)+c0s(6r+1-2x-3d cos(+)+cos(3x-2)ldr 1 4J msz+4a7r+到+若/osr-2aiz-2到 =4m(7z+到+言m3r-2)+e 装 8.求幂级数户器”的收敛半径 订 解an=器，n=1,2,3, 线 林林 =典喜鸟”装-(+)-(+▣) 内 所以该幂级数的收敛半径为r= 答 题 无 效 数学分析四试题第5页（共8页）❈ ➽ ❶ ❙ ❽ ❑ ➹ ✟ ** ** ** ** ** ** ** ** ** ** ❈ ** ** ** ** ** ** ** ** ** ** ➽ ** ** ** ** ** ** ** ** ** ** ❶ ** ** ** ** ** ** ** ** ** 7. ➛ R cos(5x + 1) cos(2x + 3)dx ✮ Z cos(5x + 1) cos(2x + 3)dx = Z 1 2 [cos(5x + 1 + 2x + 3) + cos(5x + 1 − 2x − 3)]dx = Z 1 2 [cos(7x + 4) + cos(3x − 2)]dx = 1 14 Z cos(7x + 4)d(7x + 4) + 1 6 Z cos(3x − 2)d(3x − 2) = 1 14 sin(7x + 4) + 1 6 sin(3x − 2) + c. 8. ➛➌❄ê P∞ n=1 2 n n x n ✛➶ñ➀➺. ✮ an = 2 n n , n = 1, 2, 3, · · · r = limn→∞ 2 n n 2n+1 n+1 = limn→∞ n + 1 2n = 1 2 limn→∞  1 + 1 n  = 1 2  1 + limn→∞ 1 n  = 1 2 . ↕➧❚➌❄ê✛➶ñ➀➺➃r = 1 2 . ê➷➞Û(II)➪❑ ✶ 5 ➄↔✁ 8 ➄↕