全国国贸单证员真题及其答案2006年6月

全国国贸单证员真题及其答案2006年6月（共3篇）

全国国贸单证员真题及其答案2006年6月 篇1

2009年6月全国国际商务单证员考试

国际商务理论与知识考试试题解析

一、单项选择题

1、应选C。因为市场变动剧烈因此不可能存在有效期时间长的发盘。

2、应选D。又称（Shipping Mark）唛头又称运输标志包括收货人名称的英文缩写、参照号、目的地、件号等，有的还包括原产地、合同号、体积与重量。其作用是便于装卸、运输、储存过程中识别，防止错发错运。因些装运港不是其包含内容。

3、应选A。该题为报检知识，如果产地与报关地不一致出具B或C。其中出境货物换证凭条为电子报检项下的。

4、应选C。一般出境货物在报关前或装运前7天报检，需隔离检疫的动物，出境前60天预报检，隔离前7天报检。

5、应选A。要足够的细心，本题说的是出口报检所以报检单就必须，而根据结汇的方式不同，因此信用证不是必须文件。

6、应选A。

7、应选B。

外贸企业制单之后，为保证一次性成功议付，在向银行交单前，应先行严审单据。审单时采用纵横审单法：即先将信用证从头到尾阅读一遍，每涉及到一种单据，立即与那种单据核对。以达到“单证一致”（横审）；横审完毕后，再以发票为中心，与其他单据挨个核对，特别注意各单据签发日期的合理性及共有项目的一致性，确保“单单一致”（纵审）。审核过程中，每发现一个不符点，应立即记录在审单记录表上，并在记录文字后写上“改”、“加”、“补”字。待改妥单据后，在这些字上划圈表示不再有此不符点。当全部字划圈后，单据完全改妥相符才可交单议付。

8、应选B。制单基本要求中的正确至少包括两个方面的内容：一方面是要求各种单据必须做到“三相符”。（即：单据与信用证相符、单据与单据相符、单据与贸易合同相符）；另一方面则要求各种单据必须符合有关国际惯例和进口国的法令要求和规定。和单货相符。

9、应选B。应该按信用证和合同的价格条款。10、11、12、13、14、15、应选B。90天。应选为D。将ABC作为发票的抬头人。应选为C。注意是CNY而不是RMB。应选为D。是含折扣价，CIFC中的C是英文（commission折扣的意思）。应选为C。发盘和接受是必不可少的环节，一方的发盘经对方有效接受，合同即告成立。应选B。对于一项完整的发盘一般包括：品名规格、数量、包装、价格、装运、付款、保险七大要件。其中最基本的三点是：货物名称、数量和价格。

16、应选C。贸易术语变形是解决装船及卸船费用的负担问题，但在风险责任划分上和原贸易术语没有任何区别。如FOB的各种贸易术语变形只是规定了货物的装卸或理平舱由谁负担费用，但我们的风险分界点是一样的，都是在装运港的货越船舷。17、18、应选B。CFR Landed的意思是CFR项下的卸到岸上，因些在目的港的卸货费用应由卖方负担。应选A。CIF Ex ship’s hold 是CIF术语的变形，因此它的风险转移点是在装运港的货越船舷，而DES的风险转移点是目的港的船上交货时由卖方转移给买方，因此买方在前者中的风险大。

19、应选D。CIF Liner Terms 即为CIF班轮条件。指卸货费用按班轮条件处理，即买方不负担，卖方负担。

CIF Landed 即为CIF 卸到岸上指由卖方负担将货物卸到目的港岸上为止的卸货费，包括从轮船到码头转运时可能发生的驳船费和码头捐税。CFR吊钩下交货（CFR ex tackle）。卖方负担货物从舱底吊至船边卸离吊钩为止的费用。CFR舱底交接（CFR ex ship’s hold）。指买方负担将货物从目的港船舱起吊卸到码头的费用。20、21、22、23、24、25、26、27、28、29、30、31、32、33、34、应选A。应选A。应选C。当交货地点选在目的港时，应选用DES和DEQ。应选A。应选C。托收一定排除A。应选B。应选B。银行拒收迟于运输单据出单日期21天后提交的单据，别外，单据不能迟于信用证的到期日。应选B。含佣价=净价／(1－佣金率)应选A。根据27公式选择A。应选B。银行只接受清洁提单。运用排除选项只能选B了。应选B。包装的改变不是实质上变更发盘条件，因此本题仍构成接受。合同成立。应选A。应选D。应选A。因为询盘过程中，我方以说明我方询盘的目的，而对方的发盘应充分考虑这一点，就在合理时间内有效。35、36、37、应选A。应选B。应选A。W/M意味着从重量吨和体积吨中较高收费，W=80×1500=120000KG=120TM=60×40×50CM×1500=180T，因此M较高。运费=基本运费﹢附加运费

=180×USD150×（1+35%）= 27000×1。35=3645038、普通货物的航空重量计算：（1）先求体积再除以0。006（立方米/千克）（2）比较体积重量与实际毛重；

（3）择高计算。因此本题计算M=225×0。45×0。30×0。25÷0。006=126539、40、AB

二、多项选择题

1、BC。FCA、CIP与CPT的风险转移点是货交承运人。

2、BD。FAS的风险交接点以船边为界；CPT、FCA以货交承运人为界； CIF是以装运港的货越船舷为界； DDU

是以卖方要承担将货物运至目的地的一切风险和费用。

3、CIF的风险交界点是以装运港的货越船舷，出口报关责任是卖方，进口报关责任是买方；DES的风险交界点

是指定目的港的船上；出口报关责任是卖方，进口报关责任是买方。他们的运输方式一样。所以选BD。

4、选ABC。一般附加险共11种：偷窃提货不着险；淡水雨淋险；短量险；渗漏险；混杂、玷污险；碰损、破

碎险；串味险、受潮受热险；钩损险、包装破裂险；锈损险。

5、CDE6、ABCDE7、AD。国际贸易的实质是单据之间的买卖。

8、ABD。本票和汇票的区别体现在五个方面：（1）本质不同；本票是允诺式票据而汇票是委托式票据。（2）基

本当事人不同；本票有两个即出票人和收款人而汇票有三个出票人、收款人和付款人。（3）是否需要承兑不同，本票远期无须承兑。（4）主债务人不同。本票不变，而汇票在付款人承兑前是出票人，承兑后承兑人为主债务人。（5）份数不同。本票只能一式一份，而汇票通常一式两份或多份。

9、ABC10、本题是报关题。其中进出口阶段包括：进出口申报；配合查验；缴纳税费；提取或装运货物。所以选

ABD。11、12、ABCDE。金融单据包括：汇票、本票、支票等具有货币性质；商业单据有商品属性：商业发票、海运提单、保险

单等。应选ABE。13、14、15、16、17、18、19、20、AC ABCDE ABD。信用证根据合同开出，但一经开出便是独立的文件。ABCE ABCDE。ABCD。ABC ABCDE

三、判断题

1、B．信用证支付方式下，应在发出货物前保证信用证的开到，且要无误。

2、B．只有在出口收汇核销后才能出口退税。

3、B．如果信用证中没有规定是否可以分批装运和转运，应视为可装运和转运。

4、A．

5、B．班轮运费的计算方法有重量法、体积法、从价法、选择法、综合法和按件法。对于有些货物无法衡量其重

量或测其体积，又非贵重物品，如活牲畜、汽车等均按件、只、头、辆等计算运费。

6、A普惠制产地证应持申领所需文件（如商业发票、普惠制产地证申请表等）向各口岸的检验机构或贸促会办

理，最迟于货物出运前5天办理。

7、B根据不同的收货人抬头可分为记名提单、不记名提单、空白抬头提单、指示提单。记名提单，收货人一栏

载有收货人名称，其必须由收货人本人持提单提货的提单，一般不可转让。不记名提单是指“收货人”

一栏留空不填或填持有人（TO BEARER），任何人持有该提单均可提货的提单，无须背书转让。指示提

单在收货人一栏填有“凭指示（To order）”或“凭某人指示(To order of …)”字样。其实空白抬头提单就

是不记名提单。

8、B9、B一般原产地证书(certificate of orign of the people’s republic of China),又称普通原产地证书，若合同或信用

证没有作特别规定一般应在检验检疫局出具。普惠制产地证可以由检验检疫机构或贸促会出具。

10、A．

11、A．

12、A．

13、A14、A 因为必须交正本发票和三份副本，而题只交了三份副本。

15、A16、B 运输单据中只有海运提单是物权凭证。对于多式联运提单只有有一程是海运的且抬头人写成to order 格式，对于租船合约提单在规定可以作为物权凭证的情况下才可以作为物权凭证，没有规定的是不能做物权凭

证的。

17、B装货单也叫配舱回单，在拿上配舱回单报关，海关查验后在上面签章，也叫关单，我们凭此装完货后换

取大幅收据或站场收据，然后我们再凭站场收据或大副收据去换取提单。

18、B因为FOB和CIF贸易术语的风险转移点均为在装货港，当货越船舷时。

19、B在托收项下，承兑交单是指进口方承兑后，代收行向进口人交单。

20、A此汇票为指示式抬头，既可由John Stone来收汇也可以由其经背书转让后让别人来收汇。

21、A22、BD组术语为实际性交货。

23、A24、B接受是不可以撤销的，发盘一经接受，合同即告成立，对买卖双方都有约束力，如果撤销将成为毁约。

而发盘可以在一定条件下可以撤销。

25、A26、A27、B信用证的风险小的多，再就是信用证支付方式下是以信用证规定的各种单据为支付条件而不仅是货运单

据。

28、A因为本题是从重量吨和体积吨选较大者。

29、B一张报关单可以打20项商品

30、B31、B32、A33、A34、B 应向进口方索汇

35、A36、B发票必须是具体的。

37、B必须是已装船提单。

38、A39、A40、B它可以不规定装运期，但必须规定有效期。

四、简答题

1、（1）答：出票人：CHINANATIONAL ANIMAL BYPRODUCTS IMP.&EXP.CORP.SHANGHAI BRANCH

付款人：MITSUBISHITRUST & BANKING CO.LTD., 4-5 MARUNOUCHI 1-CHOMECHIYODA-KU , TOKYO , JAPAN.（2）答：汇票是远期汇票，见票后90天付款。

（3）答：共有两份汇票。

（4）答：托收银行是中国银行上海分行。

2、答：常见的海关证明联主要包括：进口付汇证明；出口付汇证明；出口退税证明；进口货物证明书；出口收汇核销单。

3、（1）该提单的发货人应是信用证的受益人即： China National Mine Import and Export Corp.Beijing , P.R.China.但收货人要注意单据要求，应是To Order；通知人是开证申请人Nissho Twai corporation No.4-5 Akaasaka Chome Mi –Natou Tokyo , Japan.(2)由题义可是应答为运费预付。

（3）该提单是一个指示提单，也是一个清洁提单，也是一个已装船提单或顺签提单。答任一个即可。

4、答：海关发票的含义：海关发票是根据某些进口国海关的规定，由出口商填制的一种特定格式的发票，它可以供进口商凭以向海关办理进口报送、纳税等作手续。

其作用：（1）进口商凭以向海关办理进口报关，进口国海关进行估价完税的凭证。（2）进口国海关核定货物原产地，征收差别税，查核进口商品价格，决定是否征收反倾销税的依据。（3）作为进口国海关编制统计资料之用。

全国国贸单证员真题及其答案2006年6月 篇2

the place of articulation the presence or absence of vocal-cord vibration the manner of articulation ______ is generally regarded as the founder of modern linguistics.()A.Fillmore B.Saussure C.Chomsky D.Lyons

A native speaker usually possesses four types of knowledge about his own language.______ knowledge is a native speaker’s intuition about the sounds and sound patterns of his language.()A.Semantic

B.Syntactic

C.Morphological

D.Phonological

Phonetics has three sub-branches.______ phonetics is concerned with how a sound is produced by the vocal organs.A.Articulatory B.Acoustic C.Auditory D.Visual Dentals are sounds ______.()produced by both lips

produced by the contact between the upper teeth and the lower lip made with the tip of the tongue behind the upper front teeth or with the tongue tip between the upper and lower teeth articulated by raising the tip or the blade of the tongue to the alveolar ridge A phoneme is defined as ______.()a minimal meaningful unit in the grammatical system of a language a minimal distinctive unit in the grammatical system of a language a minimal distinctive unit in the sound system of a language a minimal meaningful unit in the lexical system of a language Distinctive features are used describe ______, while phonetic features are used to describe their ______()A.phonemes … allophones B.morphemes … allomorphs C.allophones … phones D.allomorphs … morphs

If ______, then they are said to be in contrastive distribution.()two sounds can occur in the same environment and the substitution of one sound for the other does not cause a change of meaning two sounds can occur in the same environment and the substitution of one sound for the other causes a change of meaning two sounds can never occur in the same environment two sounds can occur in contrastive environments The root morphemes are ______.()lexically dependent on roots and do not convey the fundamental meanings of words the most important parts of words that carry the principal meanings those that can stand by themselves as individual words never found alone as words, but are always joined with other morphemes If two sounds are ________, they are said to be allophones of the same phoneme.()in contrastive distribution and also phonetically similar sometimes in free variation in contrastive distribution phonetically similar and also in complementary distribution If two or more morphs are semantically identical and also in ______, they are said to be allomorphs of the same morpheme.()A.complementary distribution B.contrastive distribution C.free variation D.contradictory distribution Clipping refers to the process in which ______.()a compound is made by blending parts of two words words are formed by putting the initial letters of several words together a word is shortened without a change in the meaning or in the part of speech new words are created simply by changing their parts of speech The ______ relation is a kind of relation between linguistic forms in a sentence and linguistic forms outside the sentence.()A.syntagmatic B.sequential C.hierarchical D.paradigmatic In a hierarchical structure diagram of a sentence, ______ are the ultimate constituents of the sentence.（）the forms which are always present on the right side of a phrase structure rule the forms at the word-level the forms at the word-level and the phrase-level the forms connected by the two lines that are branching from the same point According to TG Grammar, in the deep structure, verbs always take the ______ form.()A.base B.present C.past D.present participle The sound ______ is a voiced post-alveolar affricate.()A.[tr]

B.[

] C.[

] D.[dr] The same phrase or sentence may have two or more interpretations depending on the hierarchical arrangement of its constituents.Such a case is called ______.()A.lexical

B.grammatical C.structural

D.syntactic According to Chomsky’s TG Grammar, the static study of sentences ______, but the dynamic study of sentences ______.()deals with two levels of structure: both surface structure and deep structure … is only concerned with one level of structure, i.e.deep structure is only concerned with one level of structure, i.e.surface structure … deals with two levels of structure: both surface structure and deep structure is only concerned with one level of structure, i.e.deep structure … deals with two levels of structure: both surface structure and deep structure deals with two levels of structure: both surface structure and deep structure … is only concerned with one level of structure, i.e.surface structure A surface structure is different from a deep structure in that ______.()a deep structure is pronounceable but a surface structure is not a surface structure is relatively abstract but a deep structure is concrete a surface structure gives the meaning of a sentence but a deep structure gives the form of a sentence a surface structure corresponds most closely to the linear arrangement of words as they are pronounced while a deep structure corresponds most closely to the meaningful grouping of words

To generate the deep structure of an English sentence, we always start with the rule: ______.()A.S(NP VP

B.S(NP AUX VP C.NP(Det AP N

D.VP(V NP ______ is an obligatory T-rule.()A.T-Passive B.T-Negation C.T-Imperative

D.T-Affix The sound [v] is ________.()A.a voiced labio-dental fricative B.a voiceless dental fricative C.a voiced alveolar fricative

D.a voiceless alveo-palatal fricative The front vowels are different from the back vowels in terms of ________.()A.the shape of the lips

B.the tongue position C.the state of the soft palate D.the tension of the muscles of pharynx The sound [e] is ______ vowel.()A.a nasal front low unrounded

B.a nasal mid back unrounded C.an oral high back rounded

D.an oral front mid unrounded 得分

评卷人

复查人

Chinese linguistics is a kind of general linguistics.______ All sounds produced by human speech organs are linguistic symbols.______ The sound [u] may be marked with [+high], [-low], [-front], [+back], [+rounded] and [-tense].______ Bilabials are different from alveolars in terms of place of articulation.______ Only short vowels /i/, //, // and // can precede final //.______ Phones are the realizations of a specific phoneme.______ A morpheme is a minimal distinctive unit in the sound system of a language.______ IC analysis is arbitrary segmentation.______ If the words or phrases in a sentence can be replaced by words and phrases outside the sentence and the resulting sentence is still grammatical, then we say the replacing forms and replaced forms have paradigmatic relations.______ Statically, we examine the process by which sentences are generated by syntactic rules.______ The substitutional relation refers to the linear ordering of the words and the phrases within a sentence.______ To generate the deep structure of an English sentence, we always start with the rule: S(NP AUX VP.______ The constituent which may be present or absent on the right side of the arrow in a PS rule is called a compulsory constituent.______ In the transformational rule T-Affix, the term “affix” refers to the affixes of main verbs.______ T-Passive must be applied before T-Yes/No question.______ 得分

评卷人

复查人

What are the five sub-branches of linguistics? Define them respectively.（7%）得分

What is the difference between segmental features and suprasegmental features? And what are the suprasegmental features in English?(6%)得分

Explain the term Labeled IC Analysis.(7%)得分

得分

评卷人

复查人

Write the symbol that corresponds to each of the following phonetic descriptions:(6%)a voiceless palatal plosive

______ a low back rounded lax vowel ______ a central liquid

_____ a high back rounded tense vowel ______ 得分

Change the following phonemic transcriptions into phonetic transcriptions:(8%)/wi:k/

____________ /`kkteil/

____________ /milt/

____________ /`kmft bl/

____________ 得分

Divide the following words into separate morphemes by placing a “+” between each morpheme and the next:(7%)Example: bookshelf = book + shelf endearment = ____________ basically = ____________ phoneme = ____________ unhappily = ____________ television = ____________ sputnik = ____________ unsuccessfully = ______ 得分

Draw the deep structure phrase marker and apply necessary transformational rules to generate the following sentence:(9%)Has the car been repaired?

得分

2006年（下）江苏省高等教育自学考试 27037语言学概论试卷答案

I.（每空1分，共10分）本项为填空题，拼写错误、大小写错误、单复数错误均不得分！

visual … auditory（本题每空1分，两空顺序不限）descriptive Palatal … velar（本题每空1分，两空顺序不可颠倒）generality free morphemes static deep … surface（本题每空1分，两空顺序不可颠倒，若两空写成同一个词，两空均不得分）II.（每题1分，共25分）

– 10: CAB 11 – 15: DACCA 16 – 20: BBDAC 21 – 25: DBADC 26 – 30: BDBDA 31 – 32: BD III.（每题1分，共15分）

– 35: FFT

– 40: TTFTF 41 – 45: TFFTF 46 – 47: FT IV.（共20分）

Linguistics has five sub-branches: phonetics, phonology, morphology, syntax and semantics.（2分）

Phonetics is the study of speech sounds of all human languages.（1分）Phonology is the science that deals with the sound system of a language.（1分）Morphology examines word formation and the internal structure of words.（1分）Syntax is concerned with how words are combined to form phrases and how phrases are combined by rules to form sentences.（1分）Semantics is the study of the meaning or words and sentences.（1分）

The distinctive features which can only have an effect on one sound segment are called segmental features.（2分）The distinctive features that can affect more than one sound segment and can also contrast meaning are called suprasegmental features.（2分）There are three kinds of them in English: stress, intonation, and juncture.（2分）

By IC Analysis, we mean that we divide the morphemes of a word or the words of a sentence into two groups and then divide each group into subgroups, and so on, until we reach single morphemes of the word or single words of the sentence.（4分）Some linguists have modified IC Analysis by labeling each constituent with a syntactic category.The revised method is called Labeled IC Analysis.(3分)V.（共30分）51.（共6分）

[c] [ ][r] [u:]

52.（共8分）

[wi:c] or [wi:c﹁] [`kh﹁tei l ] [mi l t] or [mi l t﹁] [`ch

ftb l ]

53.（共7分）

endearment = en + dear + ment basically = bas + ical + ly phoneme = phon + eme unhappily = un + happi + ly television = tele + vis + ion sputnik = sputnik unsuccessfully = un + success + ful + ly 54.（共9分）

S

NP

AUX

N Tense

Perf

V

Someone Present

have-EN

The car

Present have-EN

+ be-EN repair

Present have the car EN be-EN repair

Have Present

be EN repair EN Has been

repaired

Note:

T-Passive;

（0.5分）

T-Agent-deletion;（0.5分）T-Yes/No question;（0.5分）T-Affix

（0.5分）

VP NP

Det repair the

by someone Ø

N

car（3分）1分）1分）1分）1分）

全国国贸单证员真题及其答案2006年6月 篇3

2006/06/03

一． 求极限

解 由 an2limn222（n次复合）。

an2an1知

a122,a22a142,，2an142，an有上界； anan12an1,an1an，an单增，又an2an1,由单调有界数列必有极限知，an有极限。不妨设 limana,na2a,a2，即 limn2222。

二、xu设函数f(x)连续, 证明 f(t)dtdu0ox0(xu)f(u)du。

证 方法一 令 F(u)0u0f(t)dt, 则由分部积分法得，xx0uf(t)dtduoxF(u)duuF(u)0x0xuF(u)du

xF(x) 方法二 令 F1(x) F2(x) 因为 F1(x) F2(x)x0uf(u)duxf(t)dt0x0uf(u)du

x0xf(u)dux0uf(u)dux0x0(xu)f(u)du。(xu)f(u)du x0x0uf(t)dtdu, F(x)2o(xu)f(u)duxx0f(u)dux0uf(u)du

x0x0f(t)dt

f(u)duxf(x)xf(x)x0f(t)dt

所以F1(x)F2(x)C.又由于F1(0)F2(0)0,所以C0.xu因此, f(t)dtdu0ox0(xu)f(u)du。

三．若函数f(x)在闭区间[2,4]上有连续的导数,且f(2)f(4)0,试证明:

42f(x)dxmaxf(x)2x4

证法一 利用拉格朗日中值定理 f(x)f(x)f(2)f(1)(x2),1(2,x)

f(x)f(4)f(x)f(2)(4x),2(x,4)

f(x)M(4x)，f(x)dx 若记 Mmaxf(x), 则有 f(x)M(x2),2x44242323243所以 f(x)dxf(x)dxf(x)dxM(x2)dx3243M(4x)dx

2M2(x2)22x4(4x)M

34证法二 记Mmaxf(x), 对于任意实数c, 42f(x)dx42f(x)d(xc)

4[(xc)f(x)]242(xc)f(x)dx

42xcf(x)dxM42xcdx

令 c3, 则有 42f(x)dxM42x3dxMmaxf(x)

2x4证法三 由于f(2)f(4)0,根据牛顿_莱布尼茨公式,有

f(x)x2f(t)dtx4f(t)dt

若记Mmaxf(x), 则有f(x)M(x2),2x44242323243f(x)M(4x)，f(x)dx f(x)dxf(x)dxf(x)dxM(x2)dx43M(4x)dxM

四． 设函数fx在0,1上具有二阶导数，且f(0)f(1)0，证明 存在0,1，使f2f1。

证

令 Fx1xfx，F(0)F(1)0，在0,1上用罗尔定理知，存在0,1，使 F1ff0。

再令Gx1xfxfx，G()G(1)0，在,1上再用罗尔定理知，存在,10,1，使G()0，即 f2f1。

五． 证明：曲面xyza3（a0为常数）上任意点处的切平面与三个坐标面

所形成的四面体的体积为常数。

证 令 Fx，y，zxyza3

则Fxyz，Fyxz，Fzxy

设x0，y0，z0为曲面xyza3上的任意一点，则在该点处的切平面方程为

y0z0xx0x0z0yy0x0y0zz00

化为截距式，有

x3x0y3y0z3z01

所以，所求四面体的体积为

V 163x03y03z092x0y0z092a3

即所求体积为常数。

六．判别级数

1!22!23!2n!2 2n!n1的敛散性。

解

0un1!22!23!2n!22n!n1n1!22n1!2nn!2n!n!2n!2n!2n!22n!14nn!22n!vn

而 limvn1vnnlimnn13limnn2n12n21

所以，由比值判别法，知级数vnn12n!n1nn!2收敛。

再由比较判别法知级数unn11!22!23!2n!22n!n1收敛。

七．设函数f(x)在(,)上连续可导，求

1yf(xy)L2 ydxxy2[yf(xy)1]dy2，其中L为从点A(3,)到B(1,2)的直

323 线段。

解 令P1yf(xy)y22，Qxy2[yf(xy)1]

PyQx[2yf(xy)xy2f(xy)]y1yf(xy)y2=

23yf(xy)xyf(xy)1y2

1y2[yf(xy)1]2xy2[yf(xy)]323yf(xy)xyf(xy)1y2

PyQx，故原积分与路径无关，选取路径ACCB，yB ∴原式=CBAC=2321y1[yf(y)1]dy221323[149f(23x)]dx

CoAx [23323f(231x)]dx2223[f(y)1y2]dy

23xu

32x332f(u)du223f(y)dy1y4。

23八． 设半径为R的球的球心在以原点为中心，半径为a2aR0的定球面上点0,0,a处，当R等于多少时前者夹在定球面内部的表面积最大？其中a为常数。

解

定球球心在以原点，半径为R的球的球心在0,0,a，则两球面方程分别为

x2y2z2a2,消去z，得

xy22xyzaR

2222R224a4a22R222

S:zxzaxRxy，yRxy222zyRxy222S位于定球面内部的面积为

ARDxyzz1ydxdyxRRxyR2a04aR2222Dxy222dxdy

02RRr22rdrdθ

2RAR4R2Ra33Ra200舍去

RAR44343a,R