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习题1-7
1(1)5)21413(lim )243(lim 2
1
2
1
=-+⨯=-+→→x x x x
(2)93
252lim 35lim 2
222-=-+=-+→→x x x x (3)0
1
)3(3)3(lim
1
3lim
2
2
3
2
2
3
=+-=+-→→x x x x
(4)01
11
1lim 11lim 1
12lim 112
2
1
=+-=+-=-+-→→→x x x x x x x x (5)2)002(lim )1
12(lim )112(lim 22=+-=∞
+∞-=+-∞→∞→∞→x x x x x (6)4
23
22
4
2
/1)3/(11/1/1lim
1
3lim x x x
x x x x x x x +-+=+-+∞→∞
→
000100lim /1)3/(11/1/1lim 423
2
=+-+=∞
+∞-∞
+∞=∞→∞→x x (7)3
2
1424lim 12lim
4
586lim
442
2
4=--=--=+-+-→→→x x x x x x x x x
(8)2
123124lim 2324lim 2
02
2
3
=++-=++-→→x x x x
x x x x x x (9)x h x h
x
h x h h 2)2(lim )(lim 02
2
0=+=-+→→ (10)2)1
122(lim )12)(11(lim 322=--+=-+∞→∞→x
x x x x x x
(11)x
x
x
x
e
e e
e x --+≤
+≤
1cos 0
cos lim
1lim
0-=+=+∴∞++∞++∞→-+∞→-+∞→-x
x
x x
x
x x
x
x
x
e
e x e
e e e e e x 故趋向于故趋向于，趋向于时，当
(12)
5
2334sin 5
233402
2
+--≤
+--≤
x x x x x x x
sin 5
233
4lim
/5/23/3/4lim
5233
4lim
2
2
22
=+--=+--=+--+∞→+∞→+∞→x x x x x
x x
x x x
x x x x 故
(13))448318(lim 231lim 323
838x x x x x x x x x +++÷+---=+---→-→ 23
)8(1)
8(824lim 3
144lim 32
38
32
3
8
-=+---+---
=+-++-=-→-→x x x x
x
(14)∞
==-⨯+=-+→→→0
16
lim )
22(222lim
)
2(2lim
22
2
32
2
2
3
2
x x x x x x (15)x
x x x x x x x x x x x ++++-+=-++∞
→+∞
→2
2
2
2
1)
1)(1(lim
)1(lim
211
1)/1(1lim
1lim
2
2
=++=++=+∞
→+∞
→x x
x x x x
(16)0arctan lim 2arctan =∴∞→≤∞→x
x
x x x ，，π
(17))
1)(1()2)(1(lim )1311(
lim 2131++-+-=---→→x x x x x x x x x 11
1121lim 1
2lim 2
1
2
1
-=+++-
=+++-=→→x x x x x
(18)50
20
30
50
20
30
)
/12()
/23()/12(lim
)
12()
23()12(lim
x x x x x x x x +--=+--∞
→∞
→
2020
50
20
30
50
20
30
23
lim
2
3
2
lim
)
02()
03()02(lim
∞→∞
→∞
→=⨯=+--=x x x
(19))11(lim 2
2
+--++∞
→x x x x x
1
1)
11)(11(lim
2
22
2
2
2
+-++++-++++--++=∞→x x x x x x x x x x x x x
2
2
2
2
/1/11/1/112
lim
1
12lim
x
x x x x x x x x
x x +-+++=+-+++=∞
→∞
→
10
010012
lim
=+-+++=∞
→x
2(1)5
1
5)/31)(/21)(/11(lim
5)
3)(2)(1(lim 3
=+++=+++∞→∞
→n n n n
n n n n n
(2)∞=-⨯+-=-⨯+-=+-∞→∞→∞→∞→∞
→)1(lim /11/11lim )1(lim 11lim 1
)1(lim 2
n n n
n n n n n n n n n n
