同濟(jì)高數(shù)第六版課后習(xí)題答案

1、同濟(jì)六版高等數(shù)學(xué)課后答案全集第一章習(xí)題1?11?設(shè)A?(????5)?(5???)?B?[?10?3)?寫(xiě)出A?B?A?B?AB及A(AB)的表達(dá)式?解A?B?(???3)?(5???)?A?B?[?10??5)?AB?(????10)?(5???)?A(AB)?[?10??5)?2?設(shè)A、B是任意兩個(gè)集合?證明對(duì)偶律?(A?B)C?AC?BC?證明因?yàn)閤?(A?B)C?x?A?B?x?A或x?B?x?AC或x?BC?x?AC?BC?所

2、以(A?B)C?AC?BC?3?設(shè)映射f?X?Y?A?X?B?X?證明(1)f(A?B)?f(A)?f(B)?(2)f(A?B)?f(A)?f(B)?證明因?yàn)閥?f(A?B)??x?A?B?使f(x)?y?(因?yàn)閤?A或x?B)y?f(A)或y?f(B)?y?f(A)?f(B)?所以f(A?B)?f(A)?f(B)?(2)因?yàn)閥?f(A?B)??x?A?B?使f(x)?y?(因?yàn)閤?A且x?B)y?f(A)且y?f(B)?y?f(A)?

3、f(B)?所以f(A?B)?f(A)?f(B)?4?設(shè)映射f?X?Y?若存在一個(gè)映射g?Y?X?使??其中XIfg??YIgf??IX、IY分別是X、Y上的恒等映射?即對(duì)于每一個(gè)x?X?有IXx?x?對(duì)于每一個(gè)y?Y?有IYy?y?證明?f是雙射?且g是f的逆映射?g?f?1?證明因?yàn)閷?duì)于任意的y?Y?有x?g(y)?X?且f(x)?f[g(y)]?Iyy?y?即Y中任意元素都是X中某元素的像?所以f為X到Y(jié)的滿射?又因?yàn)閷?duì)于任意的x1

4、?x2?必有f(x1)?f(x2)?否則若f(x1)?f(x2)?g[f(x1)]?g[f(x2)]?x1?x2?因此f既是單射?又是滿射?即f是雙射?解由3?x?0且x?0得函數(shù)的定義域D?(???0)?(0?3)?(9)y?ln(x?1)?解由x?1?0得函數(shù)的定義域D?(?1???)?(10)?xey1?解由x?0得函數(shù)的定義域D?(???0)?(0???)?7?下列各題中?函數(shù)f(x)和g(x)是否相同？為什么？(1)f(x)?

5、lgx2?g(x)?2lgx?(2)f(x)?x?g(x)??2x(3)??334)(xxxf??31)(??xxxg(4)f(x)?1?g(x)?sec2x?tan2x?解(1)不同?因?yàn)槎x域不同?(2)不同?因?yàn)閷?duì)應(yīng)法則不同?x?0時(shí)?g(x)??x?(3)相同?因?yàn)槎x域、對(duì)應(yīng)法則均相相同?(4)不同?因?yàn)槎x域不同?8?設(shè)?求????(?2)?并作出函數(shù)y??(x)????????3||03|||sin|)(???xxxx)6

6、(??)4(??)4(???的圖形?解????21|6sin|)6(?????22|4sin|)4(?????22|)4sin(|)4(???????0)2(???9?試證下列函數(shù)在指定區(qū)間內(nèi)的單調(diào)性?(1)?(???1)?xxy??1(2)y?x?lnx?(0???)?證明(1)對(duì)于任意的x1?x2?(???1)?有1?x1?0?1?x2?0?因?yàn)楫?dāng)x1?x2時(shí)??0)1)(1(112121221121??????????xxxxxx