26.-Flight MU257 _______________ . I must be off now.
-Have a nice trip.
A. is being announced B. has announced
C. was announcing D. had been announced
25. When _______________ comes to saving energy, big changes start with small steps, like turning off the lights.
A. that B. this C. it D. one
24. Of the two cameras, I would prefer _______________ one, which is very easy for me to carry. K.s+5-u
A. a smaller B. the smallest C. a small D. the smaller
23. Mr Jones, a professor, ___________ for his excellent lectures, is popular with his students.
A. known B. knowing C. to be known D. having known
22.-Can you give some advice on what I said just now?
-Sorry. My mind______________.
A. is wandering B. was wandering
C. has wandered D. had wandered
第一节:语法和词汇知识(共15小题;每小题1分,满分15分)
从A、B、C、D四个选项中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑。
例:It is generally considered unwise to give a child ___________ he or she wants.
A. however B. whatever C. whichever D. whenever
答案是B。
21. Having __________ no-meat day would be a good way of encouraging ___________ low carbon life-style.
A. a; the B. a; a C. the; the D. the; a
20.(本小题满分13分)
设函数
.
(1)当
时,求
的极值;
(2)当
时,求
的单调区间;
(3)若对任意
及
,恒有
成立,
求
的取值范围.
解:(1)依题意,知
的定义域为
.
当
时,
,
.
令
,解得
.
当
时,
;当
时,
.
又
,所以
的极小值为
,无极大值 .
(2)![]()
![]()
当
时,
,
令
,得
或
,令
,得
;
当
时,得
,
令
,得
或
,令
,得
;
当
时,
.
综上所述,当
时,
的递减区间为
;递增区间为
.
当
时,
在
单调递减.
当
时,
的递减区间为
;递增区间为
.
(3)由(2)可知,当
时,
在
单调递减.
当
时,
取最大值;当
时,
取最小值.
所以![]()
.
因为
恒成立,
所以
,整理得
.
又
所以
,
又因为
,得
,
所以
,所以
.
19.(本小题满分13分)在数列
中,
,
,
.
(1)证明数列
是等比数列;
(2)求数列
的前
项和
;
(3)证明不等式
,对任意
皆成立.
[解析](1)证明:由题设
,得
,
.
又
,所以数列
是首项为
,且公比为
的等比数列.
(2)解:由(1)可知
,于是数列
的通项公式为
.
所以数列
的前
项和
.
(3)证明:对任意的
,
![]()
.
所以不等式
,对任意
皆成立.
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