数学分析(复旦大学版)课后题答案18章.pdfVIP

243 1›lÙ ¹ëCþ2ÂÈ© 1. y ²µe3[ a, ∞; c, d ] S¤á|f (x, y)| F (x, y)§¿…uy ∈ [ c, d ]È©a+∞ F (x, y) dx˜—Âñ§Ka+∞ f (x, y) dx uy ∈ [ c, d ]½˜—Âñ§…ýéÂñ. y² µÏÈ©a+∞ F (x, y) dxuy ∈ [ c, d ]˜—Âñ§K d¹ëCþ2ÂÈ©…ܘ—Âñn§ A é∀ε 0§3†yÃA (ε) a§A, A A ž§é˜ƒy ∈ [ c, d ] §k F (x, y) dx ε 0 0 A A A A f (x, y) dx |f (x, y)| dx F (x, y) dx ε阃y ∈ [ c, d ]Ѥá A A A dၹëCþ2ÂÈ©…ܘ—Âñn§a+∞ f (x, y) dxuy ∈ [ c, d ]˜—Âñ§a+∞ |f (x, y)| dx uy ∈ [ c, d ]˜—Âñ Ka+∞ f (x, y) dxuy ∈ [ c, d ]˜—Âñ…ýéÂñ. 2. y ²eÈ©3¤‰½«mS˜—Âñµ (1) +∞ cos xy dx (y a 0) 0 x2 + y2 (2) +∞ cos xy dx (−∞ y +∞) 0 x2 + 1 (3) 1 ln xy dx 1 y b, b 1 b 0 y² µ cos xy 1 +∞ dx π (1) Ïy a 0§K = Âñ 2 2 2 2 2 2 x + y x + a 0 x + a 2a u´ dŸ ¼O{§ +∞ cos xy dx uy3[ a, +∞)(a 0) S˜—Âñ. 0 x2 + y2 cos xy 1 +∞ dx π (2) Ïy ∈ (−∞, +∞), = Âñ 2 2 2 x + 1 x + 1 0 x + 1 2 u´ dŸ ¼O{