1、高等數(shù)學(xué)基礎(chǔ)第一次作業(yè)點(diǎn)評(píng)高等數(shù)學(xué)基礎(chǔ)第一次作業(yè)點(diǎn)評(píng)1第1章函數(shù)第2章極限與連續(xù)（一）單項(xiàng)選擇題⒈下列各函數(shù)對(duì)中，（C）中的兩個(gè)函數(shù)相等A.，B.，2)()(xxf?xxg?)(2)(xxf?xxg?)(C.，D.，3ln)(xxf?xxgln3)(?1)(??xxf11)(2???xxxg⒉設(shè)函數(shù)的定義域?yàn)?，則函數(shù)的圖形關(guān)于（C）對(duì)稱)(xf)(????)()(xfxf??A.坐標(biāo)原點(diǎn)B.軸xC.軸D.yxy?⒊下列函數(shù)中為奇函數(shù)是（

2、B）A.B.)1ln(2xy??xxycos?C.D.2xxaay???)1ln(xy??⒋下列函數(shù)中為基本初等函數(shù)是（C）A.B.1??xyxy??C.D.2xy????????0101xxy⒌下列極限存計(jì)算不正確的是（D）A.B.12lim22????xxx0)1ln(lim0???xxC.D.0sinlim???xxx01sinlim???xxx⒍當(dāng)時(shí)，變量（C）是無(wú)窮小量0?xA.B.xxsinx1C.D.xx1sin2)ln(

3、?x點(diǎn)評(píng)：無(wú)窮小量乘以有界變量為無(wú)窮小量⒎若函數(shù)在點(diǎn)滿足（A），則在點(diǎn)連續(xù)。)(xf0x)(xf0xA.B.在點(diǎn)的某個(gè)鄰域內(nèi)有定義)()(lim00xfxfxx??)(xf0xC.D.)()(lim00xfxfxx???)(lim)(lim00xfxfxxxx?????二、填空題⒈函數(shù)的定義域是)1ln(39)(2xxxxf?????33???xxx或⒉已知函數(shù)，則xxxf???2)1(?)(xfxx?2⒊????xxx)211(lim

4、21e⒌求)1sin(1lim21????xxx解：原式=2121)1sin(lim)1(lim1)1sin(1lim111?????????????????xxxxxxxxx點(diǎn)評(píng)：正確利用兩個(gè)重要極限，將函數(shù)作適當(dāng)變形。⒍求xxx3tanlim0?解：311133cos1lim33sinlim33cos133sinlim33cos3sinlim0000????????????xxxxxxxxxxxxx點(diǎn)評(píng)：同上。⒎求xxxsin11l

5、im20???解：原式=010sin1lim11limsin)11()11)(11(lim0202220????????????????xxxxxxxxxxx點(diǎn)評(píng)：同上。⒏求xxxx)31(lim????解：原式==333131?????????????????????xxxxlimxx33343343???????????????????????xxxxlimxx==33341341?????????????????????????x

6、limxlimxxx3341????????????xxxlim===443341??????????????????????xxxlim443341??????????????????????xxxlim4?e⒐求4586lim224?????xxxxx解：原式=3212lim)1)(4()2)(4(lim44??????????xxxxxxxx⒑設(shè)函數(shù)??????????????11111)2()(2xxxxxxxf討論的連續(xù)性，并