[数学] 05年mathsub回忆题 [复制链接]

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电梯直达

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发表于 2005-11-15 12:22:20 |只看该作者 |倒序浏览

本帖最后由 sunwei0 于 2010-4-26 10:28 编辑

下面的回忆题有些是转载于本论坛网友（网名就不公开了)，剩下的是自己回忆的。

欢迎好心人
a补充、更正不完整的题目
b添加新题
c给出每道题答案

不分顺序：

1.求c=3x+5y在两条斜线和坐标轴确定的凸四边形区域内取最大值的座标

2.(1+x)^5*(2-2x)^5,find the coefficient of x^8

3.抛硬币，直到出现4种某一面为止，问不出现连续2次相同情况的概率

4.问函数y=sinx和哪个函数在x>0处有交点
y=(1+x)/2  y=ln(1+x) y=e^x  y=2+cosx  y=(2x)^0.5

5.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},+)

6.h[g(x)]=x,g(x)=f^2(x),f(2)=-1,f'(2)=3,f(1)=4,f'(1)=5,find h'(1)

7.f(x)在R上恒负，单调递增，问g(x)=f[f(x)]-f(x)f(x)单调性和正负

8.f(x)=[3sinx]在x=pi/2上的连续性

9. how many 2X2 matrices on a field of q elements are invertible

10. 400 disctinct results r obtained from 400 experiments. if 5 samples r selected with replacement, what's the probability that all 5 samples r above the mean and exactly 4 of them r in the top quartile

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

12.黎曼映照定理

13.y=sin^2(pi*x)*e^(-x),0<x<10,find the local maxim

14.两个点沿x轴和y轴运动，问.....

15.数列An满足n->+oo时n*An->1,求lim(x^n)*An,find the 收敛域

16.a,b,c,d都是整数，平均数为100，且a<b<c<d,求a+d最值

17.一道用L'hosoital法则求极限的题

19.y=x(x+b)在（0，2)上积分面积是7/3，求b

20.A和B分别是R上的开、闭区间，问哪个是开区间。{x|x属于A且不属于B}

21.已知三阶矩阵det,求其逆的det

22.设g(x)是f(t)在x^2到x上的积分函数,g'(1)。-f(1)

23.which of the following statement demonstrate that f(x) is not continuous at x0  即函数在f（x）在点X0处极限不等于c，求其表述

24.对于R上除零乘法群，哪个R->R影射是同构  y=x^3

25.求a+b+c+d最小值当正整数a、b、c、d满足4a=3b=5c=15d

26.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]

27.choose the tangent vector of z=x^2+2*y^2 at (1,1,5)

28.find out the number of connected components of e^z, |z|=1.

29.calculate the integration of a vector field.

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

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

31.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

32.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

33.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

34.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

35.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

36.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）

37.dy/dx=siny，问图象，

38.图论题，最小生成树有8种。

39.有一道说x^3+b^2*x^2+2x+3=0有几个值b使方程有整数根。

40.有一道说关于圆凸集合，交是对的，并是错的，余集也是错的。

41.有一道说某人有计算机计算（1+x^(-1/3)）^6为-27还是0，给出的选项是计算机用复数计算；计算机计算时溢出误差；函数在某点不连续；
函数在某点不可导

42.有一道说f_n均为连续，收敛到f，点点收敛，F_n=integral of f_n，对于0到1闭区间的x。然后有三个命题，答案是都对，
因为闭区间连续函数收敛到连续函数为一致收敛，所以三个极限都成立。

43.已知一函数，求其在x=1处的泰勒展开式前两项

44.问哪个计算式能被6整除  答案是11^13-1

45.当x大于等于零时函数f(x)满足x-x^3<=f(x)<=x，问f(x)在零点处导数情况