问题 解答题
已知命题P:函数f(x)=
x
x2+1
在区间(a,2a+1)上是单调递增函数;命题Q:不等式(a-2)x2+2(a-2)x-4<0对任意实数x恒成立.若P∨Q是真命题,求实数a的取值范围.
答案

若P是真,求导函数f′(x)=

1-x2
(x2+1)2
,令f′(x)>0可得-1<x<1

∵函数f(x)=

x
x2+1
在区间(a,2a+1)上是单调递增函数

a≥-1
2a+1≤1
a<2a+1
,∴-1<a≤0

若Q是真,可得a=2或

a-2<0
△<0
得:-2<a≤2,

∵P∨Q是真命题,∴P真Q假或P假Q真或P真Q真

若P真Q假,则

-1<a≤0
a≤-2或a>2
,∴a∈∅;

若P假Q真,则

a≤-1或a>0
-2<a≤2
,∴-2<a≤-1或0<a≤2

若P真Q真,则

-1<a≤0
-2<a≤2
,∴-1<a≤0

∴由P∨Q是真命题可得a∈(-2,2].

阅读理解

阅读理解。

     One day Mrs. Perry said to her husband, "Jack, there is a meeting of our ladies' club at Mrs. Young's

house at lunch time today. And I want to go to it. I'll leave you some food for your lunch. Is that all right?"

     "Oh, yes," her husband answered, "that's quite all right. What are you going to leave for my lunch?"

     "This tin of fish." Mrs. Perry said. "And there are some cold boiled potatoes and some beans here, too."

     "Good," Mr. Perry answered. "I'll have a good lunch."

     So Mrs. Perry went to her meeting. All the ladies had lunch at Mrs. Young's house, and at three o'clock

she came home.

     "Was your fish nice?" asked she. 

     "Yes, but my feet are hurting," he answered.

     "Why are they hurting?"

     "Well, the words on the tin were Open the tin and stand in hot water for five minutes."

1. Mrs. Perry went to the meeting because _____. [ ]

A. she had something to do with the ladies' club

B. she was a member of the ladies' club

C. she wanted to join the club

D. she was a friend of Mrs. Young's

2. Mrs. Perry left home some food for Jack's lunch because _____. [ ]

A. she didn't cooking

B. Jack knew nothing about cooking

C. she wanted Jack to have a good time

D. she wanted to go to the meeting very much

3. Which of the following is not true? [ ]

A. Mrs. Perry arrived at Mrs. Young's before lunch

B. Mr. Perry had a good lunch

C. Mrs. Perry wanted to test her husband

D. Mr. Perry liked fish

4. Jack had his feet hurt _____. [ ]

A. when he was opening the tin

B. when he was helping himself to the fish

C. before he opened the tin

D. after he opened the tin

5. "Open the tin and stand in hot water for five minutes" means _____. [ ]

A. you should open the tin and stand in hot water for 5 minutes

B. you should open the tin but not stand in hot water for 5 minutes

C. you should not open the tin but stand in hot water for 5 minutes

D. you should open the tin and let it stand in hot water for 5 minutes

单项选择题