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Binomial Theorem and Its Application in Derivation
1.(20 12 Guangdong College Entrance Examination Science T 10)

26

In the expansion of 1()xx, the coefficient of 3x is _ _ _ _ .20.

2.(20 12 Fujian College Entrance Examination Science T 1 1)4()ax Expand 3

If the coefficient x is equal to 8, then the real number A _ _ _ _ .2

3.(20 12 Hunan College Entrance Examination Science T 13) (

2x- 1x

) The constant term in the binomial expansion of 6 is

.

- 160

4.(20 12 Zhejiang College Entrance Examination Science T 14) If the function f(x)=x5,

It is expressed as f (x) = A0+a1(1+x)+a2 (1+x) 2+…+a5 (1+x) 5.

, where a0, a 1, a2, …, a5 are real numbers, then A3 = _ _ _ _ _. 10/0.

5.(20 12) Science of Shaanxi College Entrance Examination T12 5

() 2-inch shaft expansion

The coefficient of x is 10, so the value of real number a is

. 1

6.(20 10 Shaanxi college entrance examination science T4) 5 () a

xx

(xR) If the coefficient of 3x in the expansion is 10, then the real number A is equal.

Yu (

)

(1)-1

(2)

1

2

(C) 1

(D)2

7.(20 10 Liaoning College Entrance Examination Science T 13) 2

6 1( 1)()xxxx

The constant term in the expansion is _ _. -5

8.(20 10 Anhui College Entrance Examination Science T 12) 6

xyy

x

In the expansion, the coefficient of 3x is equal to _ _. 15.

9.(20 10

Hainan college entrance examination science T3) curve 2

The tangent equation of xyx at points 1 and 1 is (

)

(1) 2 1yx

2 1yx

23yx

22yx

10.(20 10 Shandong College Entrance Examination Science T7) by curve y=2

x,y=3

The graphic area surrounded by x is (

)

(1)

1

12

(2)

14

(3)

13

(4)

7 12

1 1.(20 10 Liaoning college entrance examination science T 10) The known point p is on the curve y=4 1.

Xe is the tangent of the curve at point p.

The tilt angle of, then the value range of is (

)(A)[0,4]

(B)[,]42

(C)3(,)24

(4)

3[,)4

12.(20 10 Hunan College Entrance Examination Science T4)4

2 1dxx

Equal to (

)(A)2ln2

(B)2ln2

(C)ln2

(D)ln2

13.(20 10 Jiangsu college entrance examination T8) function y = x2(x & gt;; 0) At point (ak, ak2

The abscissa of the intersection of tangent at and x axis is ak+ 1, kN.

Where, if a 1= 16, the value of a 1+a3+a5 is _ _ _ _ _ _ _ .21.

14.(20 13 Hubei college entrance examination science T 1) In the complex plane, the complex number z = i.

1i2(i is an imaginary number) * * * yoke plural pairs

The corresponding point is located at (

) A. The first quadrant

B. The second quadrant

C. the third quadrant

D. the fourth quadrant

15.(20 13 T9 of Tianjin College Entrance Examination) It is known that A, B ∈ R and I are imaginary units. If (a+i)( 1+i)=bi, then a+bi=

.

1+2i

16.(20 13 Chongqing College Entrance Examination Science T 1 1) Known complex number 5 12izi.

(I is an imaginary unit), then z.

.

five

2

17.(20 13 Chongqing College Entrance Examination Liberal Arts T 1 1) Given the complex number 12zi(i is an imaginary unit), then z.

.5

18.(20 13) Set m∈R, m2+m-2+ (

M2- 1)i is a pure imaginary number, where I is an imaginary unit, then m=

.

-2

19.

(20 13 Hubei college entrance examination liberal arts T 1 1) I is an imaginary unit, let a complex number 1z, and the corresponding points of 2z on the complex plane are symmetrical about the origin. If 123iz, then 2z.

.

-2+3i

20.(20 13 Jiangsu college entrance examination mathematics T2) let 2)2(iz(i is an imaginary unit), then the modulus of the complex number z is

.5

2 1.(20 10) The function f(x)=ln( 1+x)-x+2 is known.

2kx,

(k≥0)。

(1) When k=2, find the tangent equation of curve y=f(x) at point (1, f( 1));

(2) Find the monotone interval of f(x).

22.(20 10 Anhui college entrance examination liberal arts T20) Set the function sincos 1fxxxx, 02x, and find the monotone interval and extreme value of the function fx.

23.(20 10 Beijing college entrance examination liberal arts T 18)

Let function 3

2()(0)3

afxxbxcxda

, (0)a, the two roots of equation' () 90fxx are 1, 4 respectively.

(1) When a=3 and the curve () yfx passes through the origin, find the analytical formula of () fx;

(2) If () fx is at (,) infinity, find the value range of A.