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?k?? (5)(2k??,2k??3?2(k?0,?1,?2,?) (k?0,?1,?2,?)
?5?)3 (6)[?1,3] 2.6,6?3.,121,6?(x0?h)2 2922,,0 225.(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，该函数为非奇非偶函数. (7) 非奇非偶函数 (8)奇函数
6.(1)是周期函数，T?2? (2)是周期函数，T?4 (3)是周期函数，T?4 (4)不是周期函数
?dx?b1x (2)y?arcsin cx?a32x (3)y?ex?1?2 (4)y?log2
1?x7.(1)y?ex?e?x (5)y?
2
8.(1)y?u,u?a?x2 (2)y?eu,u?x2 (3)y?lgu,u?cos (4)y?u2,u?tgv,v?6x (5)y?arctgu,u?cosv,v?ew,w?? (6)y?u2,u?lnv,v?lnw,w?x2
9.(1)[?1,1] (2)?[2k?,(2k?1)?] (3)[?a,1?a]
1 2xk?z (4)若0?a?1,则D?[a,1?a]；若a?122，则D?Ф. 10.?[?(x)]?x4，?[?(x)]?22x，?[?(x)]?22x，?[?(x)]?2x2. 11.a?4,b??1
?1,x?0?e,x?12.f[g(x)]???0,x?0，g[f(x)]??1???1,x?1
??1,x?0???e?1,x?113.V??h[r2?(h2)2],(0?h?2r)
14.V?r324?2(2???)24????2,0???2? 15.3V??r2h3[(h?r)2?r2],(2r,??)
?90,0?x?10016.(1)p???90?(x?100)?0.01,100?x?1600
??75,x?1600?30x0?x?100 (2) p?(p?60)x??,?31x?0.01x2,100?x?1600
??15x,x?1600 (3)p?21000(元)
习题1-1 (B)
1.f(x)为偶函数.
2.f(x)?x2?2,f(x?)?x2?3.f[g(x)]??3?2x24. 21?x1x1?4 x2?0,x?0?x,x?02，g[f(x)]???0,x?0?x,x?02
?1?e?x,?1?x?08.f(x)??
x??1??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)
12n?1n (3),1 (4)(n?1)?(?1)n?1,没有极限
n?2,0 (2)(?1)n?11,0 n?1 (5)
112n?1, ????(n?1)2(n?1)2(n?1)22(n?1)(n?2)2 (6)(?1),没有极限.
32.(1)17; (2)24; (3)[3.0,[]
习题1-3 (A)
3.??0.0002 4.X?397
f(x)?1 6.limf(x)?limf(x)?1,limx?0x?0?x?0??]
1??(x)不存在. lim?(x)??1,lim?(x)?1,limx?0x?0?x?0?
习题1-4 (A)
3.(1)0; (2)0; (3)0
y?0; limy?? 4.xlim??1x?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)
3; 10a?1423x; (6); (7); (8)?1.
33a2312.(1)?; (2)0; (3)?; (4)?;
441220?330 (5)50; (6) ?.
45?1,?3.(1)?0,??1,?0?a?141a?1; (2)3; (3); (4)?
32a?1mn(n?m)m; (3); (4)0; 2n131 (5)0; (6); (7); (8).
2424.(1)10; (2)
习题1-5 (B)
1.(1)2; (2)?; (3)?1212a(3?1); (4) 562?0,k?23? (5); (6)?1,k?2; (7)2; (8)0 .
2??,k?2?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； 12 (6)?2; (7)1; (8)2; (9)1; 2.(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
6.(1)3?0,m?n2; (2)??1,m?n; (3)1;
???,m?n2 (4)1; (5)a; (6)12b4.
(10)x.