习题答案 习题1-1 (A)
1.(1)(??,1)?(1,2)?(2,??) (2)[?1,0)?(0,1]
(3)(??,?1)?(?1,1)?(1,??) (4)x?k??且x??3k??5?3?2)(k?0,?1,?2,?)
(5)(2k?,2k??(k?0,?1,?2,?)
(6)[?1,3] 2.3.
126,6?19222,6?(x0?h)2
,22,,0
5.(1)奇函数 (2)非奇非偶函数 (3)偶函数 (4)奇函数 (5)奇函数
(6)当f(x)为奇函数或偶函数时，该函数为偶函数；
当f(x)为非奇非偶函数时，该函数为奇函数. (7)偶函数 (8)奇函数 6.(1)是周期函数，T (3)是周期函数，T7.(1)y??dx?bcx?a?2??4 (2)是周期函数，T?4
(4)不是周期函数
?13arcsinx2 (2)yx2
(3)y?ex?1?2 (4)y (5)y?
e?e2x?x?log1?x
8.(1)y?u,u?a?x2 (2)y?eu,u?x2
(3)y?lgu,u?cos (4)y?u2,u (5)y?arctgu,u?cosv,v?e,w??w?tgv,v?6x1x2
(6)y?u2,u?lnv,v?lnw,w?x2
9.(1)[?1,1] (2)?[2k?,(2k?1)?] (3)[?a,1?a]
k?z (4)若0?a?,则D?[a,1?a]；若a21?12，则D??.
2x10.?[?(x)]?x4，?[?(x)]?2，?[?(x)]?2，?[?(x)]?2.
2xx211.a?4,b??1
?1,x?0?f[g(x)]??0,x?0??1,x?0???h[r212.
?e,x?1?，g[f(x)]???1,x?1??1??e,x?1
13.V14.V15.Vh2?()],2(0?h?2r)
?r3224?(2???)24????2,0???2?
??rh22323[(h?r)?r],(2r,??)
16.(1)
?90,?p??90?(x?100)?0.01,?75,?0?x?100100?x?1600x?16000?x?100100?x?1600x?1600
(2)
?30x,?2p?(p?60)x??31x?0.01x,?15x,?
(3)p?21000(元)
习题1-1 (B)
1.f(x)为偶函数.
2.f(x)?x?2,f(x?21x)?x?21x2?4
3.f[g(x)]??4.8.
3?2x1?x22?0,?x,2x?0x?0，g[f(x)]???0,?x,2x?0x?0
?1?x?0x??1?1?e?x,f(x)????1,
9.g(x)?ln(1?x),(??,0]
10.奇函数，偶函数，偶函数，偶函数. 12.f(2005)?1
习题1-2 (A)
1.(1) (3) (5)
12n?1,0 (2)(?1)n?11n?1,0
nn?2,1 (4)(n?1)?(?1)n?1,没有极限
21(n?1)?2(n?1)2???n?1(n?1)2,
21(n?1)(n?2) (6)(?1)2,没有极限.
32.(1)17; (2)24; (3)[3.0,[1?]
?]
习题1-3 (A)
3.?4.Z?0.0002
?397
x?06.limx?0?f(x)?lim?f(x)?1,limf(x)?1
x?0 limx?0??(x)??1,lim?(x)?1,lim?(x)不存在.
x?0?x?0习题1-4 (A)
3.(1)0; (2)0; (3)0 4.limx??1y?0; limy??
x?1习题1-4 (B)
3.y?xcosx在(??,??)上无界，但当x???时，此函数不是无穷大.
5.当a?0,b?1时，f(x)是无穷小量； 当a?0,b为任意实数时，f(x)是无穷大量.
习题1-5 (A)
1.(1)0; (2)1; (3)1; (4) (5)
a?12310;
3a32.(1)?4; (6)3x2; (7); (8)?1.
34; (2)0; (3)?; (4)?;
41 (5)
220?350305; (6) ?.
41?1,?3.(1)?0,??1,?0?a?1a?1a?1mn(n?m)212; (2)3; (3); (4)?
34124.(1)10; (2); (3)
mn34; (4)0;
12 (5)0; (6); (7); (8).
习题1-5 (B)
1.(1)2; (2)?; (3)?21156; (4)
2a(3?1)2
?0,k?23? (5); (6)?1,k?22??,k?2?; (7)2; (8)0 .
2.??1,???1
3.a?9
4.a?1,b??1 5.不一定.
习题1-6 (A)
1.(1)2; (2)3; (3); (4)-1; (5)cosa；
21 (6); (7)1; (8)
?2; (9)1; (10)x.
22.(1)e?1; (2)e2; (3)e?2; (4)e?2; (5)e?1; (6)e2.
习题1-6 (B)
1.(1)1; (2)22?; (3)1; (4)0;
(5)0; (6)1; (7)0; (8)e?1. 2.(4)3; (5)
1?52.
习题1-7 (A)
1. 当x?0时，x4?x3比x2?x3为高阶无穷小.
2. (1)同阶，但不是等价； (2)同阶，且为等价. 3.??12
4.??m
3?0,m?n6.(1)2;
(2)??1,m?n; (3)1?2;
??,m?n (4)1a2; (5)b; (6)14.
习题1-7 (B)