高等数学(B)
及评分标准:
一. 填空题 ( 每题 3 分 )
1. 3 2.
3. 0 4.
5.
6.
7. 19/36 8. 20/21
二.选择题 ( 每题 3 分 )
1.
2.
3.
4.
5 D 6 A 7 D 8 B
三.计算题 ( 每题 7 分 )
1.
2.
;
或
3. 解法一 画出区域 D 的示意草图
解法二 画出区域 D 的示意草图
4.
(1) 当
时,
(2) 当
时,
所以本题答案是:
。
5.
6.APA-APB+BPB-BPA=E
AP(A-B)-BP(A-B)=E
(AP-BP)(A-B)=E
(A-B)P(A-B)=E ……………………2分
A-B=
……………………3分
(A-B)-1=
……………………5分
P=
=
……………………7分
7.
,
……………………3分
EMBED Equation.3
EMBED Equation.3 ~
EMBED Equation.3
……………………4分
基础解系
时,-2E-A=
EMBED Equation.3
基础解系
……………………6分
取 P=
P
P
……………………7分
8. (1). 1=
a=3 ……………………1分
(2). E
=
……………………2分
E
D
……………………3分
(3). 令T=
F
EMBED Equation.3 (y) =P (T
y) = P(
)
当y
时, F
(y)=0
当y
时, F
(y)=1
当0
函数
,
。
(2)
2.(1)
= 2k (1-k)
0
k
0 且 k
1, 即k
0且k
1时,
线性表示且表法唯一 ……………………2分
(2)当 k=1时,
若b-a=0, 则
或
……………………4分
当k=0时
若c-b-a=0时,
或
……………………6分
即当k=1 且b=a时,表法不唯一,
(c-a)
或
(c-a)
当k=0 且c=a+b时,表法不唯一,
b
或
a
(3). 当k=1且b-a
0或 k=0且c-b-a
0时,
不能由
线性表示
……………………8分
3.设销售一个零件获利为L,则
L=
……………………2分
EL= -P(
<10) + 20P (10
EMBED Equation.3
EMBED Equation.3 12) -5P(
>12)
= -
(10-
)+20[
]-5
=25
-21
-5 ……………………4分
=-25
+21
=0
25
=21
……………………6分
=
ln25-ln21-22+2μ=0
μ=11-
=11-
=11-
=11-
=10.9 ……………………8分
五1. (1) 绝对值级数
的部分和
正项级数
的部分和
(2) 用反证法,假定级数
收敛,其部分和为
设级数
的部分和为
,
则级数
的部分和
与
收敛
, 故级数
发散 。
2.设
……………………1分
即
(1)
左乘A
……………………3分
又
故
(2)
代入(1)得:
线性无关,
……………………5分
代入(2)得:
EMBED Equation.3 线性无关 ……………………7分
� EMBED Equation.3 ���
PAGE
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