数学分析(复旦大学版)课后题答案 17章.pdfVIP

240 1nÜ© ¹ëCþÈ©Ú2ÂÈ© 1›ÔÙ ¹ëCþÈ© 2 1. F (y) = yy e−x2y dx §OŽF (y). ) µÏ½n4^‡÷v§A^½n4 §k 2 y 2 −x2y −y5 −y3 5 −y5 3 −y3 1 F (y) = (−x )e dx + 2ye − e = ye − e − F (y). y 2 2 2y 2. F (y) = 0y (x + y)f (x) dx §Ù¥f (x)Œ‡¼ê§¦F (y). ) µÏf (x)Œ‡¼ê§Kf (x)ëY§u´(x + y)f (x)ëY§K½n4^‡÷v u´F (y) = 0y f (x) dx + 2yf (y)§F (y) = 3f (y) + 2yf (y). 3. eF (y) = 0 1 ln x2 + y2 dx §†OŽÈ©§¦ÑF (y)§2¦ÑF (0)§¿uA^½n4OŽF (0)( 5. 1 1 1 2 x 2 2 2 2 2 ) µy = 0ž§kF (y) = ln x + y dx = x ln x + y − dx = ln 1 + y − 1 + 0 0 0 x2 + y2 x 1 d 1 y y dx = ln 1 + y2 − 1 + y arctan . 0 1 + x2 y y ÏF (0) = 0 1 ln x dx = −1 F (y) − F (0) π F (y) − F (0) π KF+ (0) = lim = , F− (0) = lim = − y→+0 y 2 y→−0 y 2 u´F (0)Ø3 1 ∂ y ∂ 2 2 2 2 ,˜¡§x 0ž§ ln