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2012江苏考研数学三真题及答案.doc
~
=2+
2−1
'0 =
2−1=1= →− = →− 2+
→+ = →+ 2+
2−1
=1
→1=→12+
2−1=
=1
→−1= →−12+
2−1=12 =−1
=(−1)(2−2)⋯(−)
−1 −1−1!
−1 −1!
−1 −1!
−1 !
g =(2−2)⋯(−)
=(−1)g
'()=g +(−1)g''0 =g0 = −1 −2⋯(−(−1))
0 =0
'0 =→0() =→0(−1)(2−2)⋯(−)
=→0(−1)
∙→0(2−2)⋯(−)
= −1 −2⋯− −1 = −1 −1−1!
=(−1)(2−2)
' =2−2 +22(−1)'0 =1−2=−1
= −1 −1−1!
=2
(2)
=
02
()
2
2
02
2+2(2+2)
4−2
2−2
02
4−2(2+2)
2−2
02
2+2(2+2)
4−2
1+ 1−2
02
4−2 (2+2)
1+ 1−2
=2
=,=
(−1)2+2=1
02
(2)
2
2
2<<2,0<<2
0<<2
2−2<< 4−2,
02
= 02
(2)
4−2(2+2)
2
2
2−2
=1(−1) 1
=1(−1)
2−
0<≤12
1<≤32
=1(−1) 1
>32
=1(−1)
2−
12<≤1
32<<2
12>1
<2
2+2=4=2
→
(−1) 1~ 1 −12
−
1,2,3,4
1= 001 ,2= 012 ,3= 1−13
,4= −114
1,2,4
1,2,3
1,3,4
2,3,4
⇔ 1,2,⋯ =0
1 −1
1,3,4 = 0
0 −1
1
4 =0
1
3
1,3,4
−=
(+,,)
1 0 0
0 2 0
0 0 1
2 0 0
0 1 0
0 0 2
−= 1 0 0
0 1 0
0 0 2
1 0 0
0 1 0
0 0 2
2 0 0
0 2 0
0 0 1
= 1 0 0
0 0 1 =21(1)
1 1 0
−1=[()]−()=()−−()
1 0 0
0 0 2 1 0 0
0 1 1 0 0
= 1
0 0
−1 1 0
1 1 0
0 1 0
0 1 0
0
0 0 1
0 0 2
(0,1)
,
14
12
4
8
= ,,,=
+2≤1 =
1−2
3+4−2
2+2≤1 = 2+2≤1(,)
, = = 1,0<<1,0<<1,
0,
0<<1,0<<1
,
2+2≤
2+2≤1(,)
1,2(>0)
1,2,3,4
0,1
(1)
(1,1)
2(1)
1−22 ~0,1
1 1−2~0,22
2 3+4−2~0,22
~0,1
(3+4−2
)2~2(1)
3+4−2
2
2
(3+4−2
)2/1= 3+4−2
2
2
)2
(3+4−2
3 1−2 3+4−2
1−22
2
1−223+4−2
= 1−2
3+4−2~(1)
2
~
→4()
−=
1
− 2
1
()
−=[1+(−1)]
1
1
−
(1−)=→4 −1=− 2
−1
−1
−=→4
→4
→4()
−=− 2
1
= ,≥1
==
2−1,<1= ,
1
=
=
=
= = =12=12
==' 12 ∙' =2∙12==1
(0,1)=
lim→0→1,−2+−2
=(,)
2+(−1)2 =0
2−
0,1 =1
=(,)
lim→0→1,−2+−2
2+(−1)2 =0
, −0,1 =2− −1 +( 2+(−1)2) (→0
→1)
'0,1 =2,'0,1 =−1
(0,1)='0,1+'0,1=2−
=4
= =4
42
=4
= =4
2(4−)
1 4−
+ 1
= 0
=42
=
y
∗ =
=3 ∗
=−
∗ = −1
34
∗ = |∙|∗ =− 2=−27
0 1 0
0 0 1 =
=12
1 0 0
∗=12∗= 12=312
∗ = 312 =3312 =−27
=12, =13, =
,
,,
⊃
,
⊃
1−()=1223=34
=()
() = ()
15~23
lim→02−2−2cos
4
lim→02−2−2cos
4
=lim→02−2+2cos
4
=lim→02−2sin
43
lim→02−2−2cos
4
=lim→02−2+2cos
4
=lim→02−2+2(1−22!+44!+(4))
4
=lim→02−2cos∙lim→02−2+2cos−1
4
1222 = 112
=12lim→01−cos
32 =16lim→0
=lim→02−2cos∙lim→02−2+2cos−1
4
1124+(4)
=112
4
=lim→0
lim→02−2−2cos
4
=lim→02−2sin
43
=12lim→01633
=∙lim→0(2−2+2cos)
4
−~163
=lim→02−2+2cos
4
= 112
,
= ,= 1
=12 0
1
1
1(1−2)
= 0
=12(1−2)0
1+ 0
1
=−12+01− 0
1
=12
20+2
,, =, ++−50 =10000+20+24+6+22++−50
6+
(,)
, =10000+20+24+6+22
+=50
,
'=20+2+=0,
=24,=26
'=6++=0,
+−50 =0.
', =20+2
, =10000+20×24+2424 +6×26+2622 =11118
', =20+242 =32
1+1−+cos≥1+22,(−1<<1)
=1+1−+cos−1−22
' =1+
1−+ 21−2−−,
''()= 41−2+ 42
1−2 2−1−cos
41−2≥4,1+cos≤2
−1<<1
'0 =0
−1<<0
(−1,1)
0 =0
−1<<1
≥0 =0
1+1−+cos≥1+22,(−1<<1)
=1+1−+cos−1−22
(−1<<1)
≥0
' =1+1−+ 21−2−−,∈[0,1)
1+
21−2>2=+>+sin
1−>0
' >0 ∈(−1,1)
0 =0−1<<1
≥0 =0
1+1−+cos≥1+22,(−1<<1)
∈[0,1)
''()≥2>0
0<<1
' <0
'()
' >0
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