mathsub

从天而降的梦UID: 2123887

1.choose the graph of the ODE : dy/dx=Sin(y)
2.find out the number of connected components of e^z, |z|=1.
3.choose the tangent vector of z=x^2+2*y^2 at (1,1,5)
4.calculate the integration of a vector field.



1.which of the following statement demonstrate that f(x) is not continuous at x0?
2.由直线x=1,x=2,y=x,y=2围成的区域围绕着y轴旋转产生的体积
3.A is a n dimension matrix. if (A-I)^2=0
which of the following is correct:
(1)A=I
(2)detA=1
(3)tr(A)=n
4.find out the value of 'a' that make the linear system consistent?
a x+ a^2 y= a^3
x  + 2   y= 4
A.all real value except 0
B.all real value except 2
C.all real value
D.all real value except 0 and 2
E.only 0 and 2




1.A monoid is a set S with a binary operation(.) statisfy the associate law
and there exists a unity. let + and . represent the normal addition and
multiplication with real number. choose the following which is not monoid
A.(R,+)
B.(R-{0},.)
C.(R-{0},+)
D........
E.......

2.which letter is not homeomorphic to the letter C?

A.J B.N C.S D.O E.U

3.In a group S, ab!=ba, choose the possible relationship between a and b?

A.a^2=b^2 B. aba=1  C.D.E is easy to check

4.Function f is a function with two linear parts. f(0)=f(2)=0, 0<x<1,max(f)=1
choose the range of the length of f?
A.(2*2^0.5, 1+5^0.5)
B.(2*2^0.5, 1+5^0.5]
C.[2*2^0.5, 1+5^0.5)
D.[2*2^0.5, 1+5^0.5]
E. cannot remmember now.




1.What is the new function of the graph of y=4x+5 under of tranformation of
(x,y)->(3x, 3y)?

A.y=12x+5
B.y=4x+15
C.3y=12x+5
D.3y=4x+5
E.3y=4x+15

2.choose the possible 'a' that the linear equations have a root?
x+2y+3z=a
4x+5y+6z=a^2
7x+8y+9z=a^3

3.choose the possible 'p' that make the following polynomial have a integer root?
x^3-p*x^2-2*x+3=0

4.Choose the formula of the volume of the intersection of x^2+y^2+z^2=4 and
r=2 Cos(theta) (under the 柱坐标）