北大版高等數(shù)學課后習題答案

1、1習題習題1.12222222222222222223.33.33.33132.961912431.39333..pppqpqpqqppkpkpkkpkkppkkqqkqpqppaapabpapbbb???????????????????證明為無理數(shù)若不是無理數(shù)則為互素自然數(shù)除盡必除盡否則或除將余故類似得除盡與互素矛盾.設是正的素數(shù)證明是無理數(shù)設為互素自然數(shù)則素證2.證1.2222222...:(1)|||1|3.(2)|3|2.013

2、221(10)011313(01)11332(132).(10)(01)papaapkpkpbpkbpbabxxxxxxxxxxxxxxxX????????????????????????????????數(shù)除盡故除盡類似得除盡此與為互素自然數(shù)矛盾.解下列不等式若則若則若則3.解(1)222(132).(2)232151||51||5(15)(51).(1)||||||(2)||1||||1.(1)|||()|||||||||||||||

3、.(2)|||()||||||xxxxxabababababaabbabbabbababababbabb???????????????????????????????????????????設為任意實數(shù)證明設證明證4.|1.(1)|6|0.1(2)||.60.160.1.5.96.1.(6.1)(5.9).(2)0()()00().1101.11.11nnnnxxalxxxxXlXalallxalXaaannaabaa?????????

4、??????????????????????????????????????????解下列不等式或或若若若若證明其中為自然數(shù)若顯然解(1)證5.:6.120000(1)(1)(1).()().110.|.()|10|.10(1)1010(1)10110nnnnnnnnnnnnnabbnaababnbamAAmAabABCBAxxbCAxxaBmmCbamm????????????????????????????Z?設為任意一個開區(qū)間證明

5、中必有有理數(shù)取自然數(shù)滿足考慮有理數(shù)集合=若則中有最小數(shù)=證7.()().110.2|.10nnnnababmnbaAm?????Z此與的選取矛盾.設為任意一個開區(qū)間證明中必有無理數(shù)取自然數(shù)滿足考慮無理數(shù)集合以下仿8題.8.證習題習題1.232010303030002232211121(23)(22)2(6)lim1.(21)2112(7)limlim1.(11)13132(8)limlimlim11(1)(1)(1)(1)(1)(2)l

6、imlim(1)(1)xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx??????????????????????????????????????????????????????214442100(2)31.(1)3123(123)(2)(123)(9)limlim2(2)(2)(123)(28)(2)244lim.63(4)(123)(1)1(1)12(10)limlimlim.1(11)limxxxnnnxyy

7、xxxxxxxxxxxxxxxxnnnyyyxynxyyx?????????????????????????????????????????????????A???22221011001001010010142211lim0.11(12)lim(0).(13)lim(0)0.818(14)limlim1xmmmmnnnxnnmmmnnxnxxxxxaxaxaabbxbxbbabmnaxaxaabnmbxbxbmnxx??????????

8、???????????????????????????????????????????A?421.11xx??33202233333322023333220333322033331312(15)lim(1312)(13131212)lim()(13131212)5lim(1)(13131212)55lim.3(1)(13131212)(16)0lxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxa?????????????