高等數(shù)學(xué)?？茝?fù)習(xí)題及答案

1、高等數(shù)學(xué)期末試卷高等數(shù)學(xué)期末試卷一、填空題（每題一、填空題（每題2分，共分，共30分）分）1函數(shù)的定義域是.1142????xxy解.。)2[]2(??????2若函數(shù)，則52)1(2????xxxf?)(xf解.62?x3________________sinlim????xxxx答案：1正確解法：101sinlim1lim)sin1(limsinlim????????????????xxxxxxxxxxx4.已知，則________

2、__。22lim222??????xxbaxxx?a?b由所給極限存在知得又由024???ba42???ab23412lim2lim2222?????????????axaxxxbaxxxx知82???ba5.已知，則__________。??????)1)((lim0xaxbexx?a?b即??????)1)((lim0xaxbexx?01)1)((lim0???????babexaxxx10???ba6函數(shù)的間斷點(diǎn)是x?。?????

3、????0101sin)(xxxxxxf解：由是分段函數(shù)，是的分段點(diǎn)，考慮函數(shù)在處的連續(xù)性。)(xf0?x)(xf0?x因?yàn)?)0(1)1(lim01sinlim00????????fxxxxx所以函數(shù)在處是間斷的，)(xf0?x又在和都是連續(xù)的，故函數(shù)的間斷點(diǎn)是。)(xf)0(??)0(??)(xf0?x7.設(shè)則??????nxxxxy???????21????1ny(1)!n?8，則。2)(xxf?__________)1)((??

4、?xff二、單項(xiàng)選擇題（每題二、單項(xiàng)選擇題（每題2分，共分，共30分）分）1函數(shù)（）)10(11)(?????aaaaxxfxxA.是奇函數(shù)；B.是偶函數(shù)；C.既奇函數(shù)又是偶函數(shù)；D.是非奇非偶函數(shù)。解：利用奇偶函數(shù)的定義進(jìn)行驗(yàn)證。)(11)1()1(11)()(xfaaxaaaaxaaxxfxxxxxxxx?????????????????所以B正確。2若函數(shù)，則（）221)1(xxxxf????)(xfA.；B.；C.；D.。2x2

5、2?x2)1(?x12?x解：因?yàn)?，所?)1(212122222????????xxxxxx2)1()1(2????xxxxf則，故選項(xiàng)B正確。2)(2??xxf3設(shè)，則=（）1)(??xxf)1)((?xffAxBx1Cx2Dx3解由于，得＝1)(??xxf)1)((?xff1)1)((???xf2)(?xf將代入，得=1)(??xxf)1)((?xff32)1(????xx正確答案：D4已知，其中是常數(shù)，則（）0)1(lim2??

6、????baxxxxab(A)(B)11??ba11???ba(C)(D)11???ba11????ba解.????011lim)1(lim22??????????????xbxbaxabaxxxxx?答案：C11001?????????babaa5下列函數(shù)在指定的變化過程中，（）是無窮小量。A.e1xx()??；B.sin()xxx??；C.ln()()11??xx；D.xxx???110()解：無窮小量乘以有界變量仍為無窮小量，所以