文登考研數(shù)學(xué)--高等數(shù)學(xué)--習(xí)題集及其答案

1、1第一章第一章函數(shù)極限連續(xù)函數(shù)極限連續(xù)一.填空題1.已知定義域為___________.__________)(1)]([sin)(2????xxxfxxf??則解.21)(sin)]([xxxf?????)1arcsin()(2xx???1112????x2||202???xx2設(shè)則a=________.?????????????ataxxdttexx1lim解.可得=所以a=2.????atadtteeaatteaeaete????

2、?)(3.=________.?????????????????nnnnnnnnn2222211lim?解.nnnnnnnnnn?????????22221?nnnnnnnn?????????2222211?11211222?????????nnnnnnn?所以nnnn?????221?nnnnnnnn?????????2222211?1212?????nnn?(n??)212)1(2122??????????nnnnnnnnn?(n?

3、?)2112)1(12122??????????nnnnnnn?所以=?????????????????nnnnnnnnn2222211lim?214.已知函數(shù)則f[f(x)]_______.????01)(xf1||1||??xx解.f[f(x)]=1.5.=_______.)3(limnnnnn?????解.nnnnnnnnnnnnnnnnnn?????????????????3)3)(3(lim)3(lim=233lim?????

4、????nnnnnnnnn6.設(shè)當(dāng)?shù)?階無窮小則xbxaxexfxx為時?????11)(0.___________??ba32.設(shè)函數(shù)則f(x)是xexxxfsintan)(???(a)偶函數(shù)(b)無界函數(shù)(c)周期函數(shù)(d)單調(diào)函數(shù)解.(b)是答案.3.函數(shù)在下列哪個區(qū)間內(nèi)有界2)2)(1()2sin(||)(????xxxxxxf(a)(－10)(b)(01)(c)(12)(d)(23)解.42sin)0(42sin)0()(li

5、m)(lim01???????????ffxfxfxx所以在(－10)中有界(a)為答案.4.當(dāng)?shù)臉O限112111????xexxx函數(shù)時(a)等于2(b)等于0(c)為(d)不存在但不為??解..(d)為答案.??????????????????01001)1(lim11lim1111121xxexexxxxxx5.極限的值是????????????????222222)1(12325213limnnnn?(a)0(b)1(c)2(d

6、)不存在解.????????????????222222)1(12325213limnnnn?=所以(b)為答案.1)1(11lim)1(1131212111lim2222222???????????????????????????nnnnn?6.設(shè)則a的值為8)1()1()1(lim502595??????xaxxx(a)1(b)2(c)(d)均不對58解.8==502595)1()1()1(lim?????xaxxx10050255

7、9595)1()1()1(limxxxaxxxx?????=所以(c)為答案.5502595)11()1()11(limaxxaxx??????58?a7.設(shè)則??的數(shù)值為???????????)23()5)(4)(3)(2)(1(limxxxxxxx(a)?=1?=(b)?=5?=(c)?=5?=(d)均不對3131531解.(c)為答案.8.設(shè)則當(dāng)x?0時232)(???xxxf(a)f(x)是x的等價無窮小(b)f(x)是x的同階