2015考研數(shù)學(xué)一沖刺大練兵模擬測(cè)試題

2014考研數(shù)學(xué)秋季大練兵模擬測(cè)試卷（數(shù)學(xué)一）

本試卷滿分150，考試時(shí)間180分鐘

1 8 4 32

.

x ,x0

1 f(x)ln2|x| f(n)(0) n

0 ,x0

A 0 B 1 C 2 D 3

2 f(x),g(x) (,) xx1 f(x) xx2 g(x)

A x1x2 f(x)g(x) xx1

B x1x2 f(x)g(x) xx1 xx2

C x1x2 f(x)g(x) xx1

D x1x2 f(x)g(x) xx1 xx2

3 zx(x0,y0)0和zy(x0,y0)0 zz(x,y) (x0,y0)

A B

C

4 4

1

11dx1

D

12

1x2 x1

1 x2x4dx1x 2

2 1

1 1x

dx0

1 1xt 12 2

3 1xdx 2tdt

0 0 3

b

4 f(x) [a,b] [a,b] af(x)dxf()(ba)

A 1 B 2 C 3 D 4

1 2 3 0 0 1

5 A4 5 6,P0 1 0

7 8 9 1 0 0

1 0 0

Q1 1 0

0 0 1

(P1)2008A(Q2009)1

800510007 12009

4 5 6

4019 2 3

10049 5 6

A 7 8 9 B 16079 8 9

1 2 3 1 2003 3

2005 4007 6009 4 8009 6

C 7 8 9 D 7 14015 9

6 A 43 r(A)1,1,2,3 AxbAx0 ?

A 123 B 1223

C 12,23 D 21,32

7 X Y (i1,2,3,4) XX1 X2 YY1 Y2

i i X X Y Y

3 4 3 4

P|X|0,|Y|00.4,P|X|0P|Y|00.6 |X||Y|

X Y pPmax|X|,|Y|0 p

0.2 0.6 0.16 0.64

1 2 3

n

8 X N(0,2),X,X,X X X

X,S2 F F(1,n1)

2 2

F(n1)X

2

S2

F(n1)X

FnX

S2

X

2

F

S2 S2

914 4 24 .

1

9 lim(1x)xe

x0 x

10 y x0x1 x

n 2n1

n1

11 2n(3)nx R

12 z2x2y2(0z1) xyzdxdy

13 1,1T,0,1T 2,1T,1,3T , X1,1T

1 2

1,2

14 X

ab

1 2 1 2

Y .

(x2)2

f(x)Ae 4 YaXb N(0,1)

15—23 94 . .

.

15 10 xn

n

limx

n

xn1

xn1,

2 xn

x00, n0,1,2,3, , {xn}

16 10 fx,y 0,0 lim fx,y1 1

y0

x0lncos x2y2

f0,0

1

x

2 f(x,y)

f0,0

y

0,0

f(x,y) 0,0

dfx,y

(0,0)

17 計(jì)算I yey2dx(xey22xy2ey2)dy.其中C為y 從O(0,0)到A(1,1)的曲線段

C

y 2z 2z

18 10 zf

x

x0 0

x2 y2

fu

(1)n1

n1

19 10 n(2n1)3n

20 11

x1 λx2 μx3 x40,

2x x x 2x0,

3x1 (2λ2)x (4μ3)x 4x41,

(1,1,1,1)T

( )

( )

x2x3

1 2 3 4

21 11 f(x,x,x,x)ax22x22xx2xx

1 2 3 4 3 4 12 34

A

a

fxTA2x

fxTA2x

22 11 X,Y D

D(x,y)|0yx2y

XY