| 已知函数f（x）=sinx，x∈R （1）函数g（x）=2sinx•（sinx+cosx）-1的图象可由f（x）的图象经过怎 样的平移和伸缩变换得到； （2）设h(x)=f(
在R上的最小值是-
|
（1）g（x）=2sin2x+sin2x-1=sin2x-cos2x=
sin(2x-2
)π 4
先将f（x）的图象向右平移
个单位长度得到y=sin(x-π 4
)的图象；π 4
再将y=sin(x-
)图象上各点的横坐标变为原来的π 4
倍，得到1 2
函数y=sin(2x-
)的图象；最后将曲线上各点的纵坐标变为π 4
原来的
倍得到函数g（x）的图象．2
（2）h（x）=cos2x-4λcosx=2cos2x-4λcosx-1=2（cosx-λ）2-2λ2-1
∴
或λ＜-1 1+4λ=- 3 2
或-1≤λ≤1 -2λ2-1=- 3 2 λ＞1 1-4λ=- 3 2
∴λ=±
．1 2
| 完形填空。 | ||||
| One student took a box of chicken to class. Another carried on a cell-phone 1 and still another whistled loudly every time the 2 turned his back. Reform school? No, College. More and more, professors say, they are coming across 3 students in their classrooms. Many of today's young scholars (学者) arrive late, leave 4 , talk loud or take care of personal 5 such as paying bills during class. Why are the students behaving badly? "Because they can," said a student of University of North Texas. "A lot of the time, the professors let them get 6 with it." Some educators say it is time to bring politeness back to their classrooms-and even 17 taking some of the blame for bad behavior. They say that rude students are by no means the majority but that one of them can ruin an entire 8 . People are 9 when they learn that impolite behavior is becoming more and more common in 10 education, says Dr. Gerald Amanda, a counselor at City College of San Francisco. They 11 some high school students to misbehave but think those who get to 12 will behave more politely. Dr. Amanda believes that society in 13 has become more tolerant (容忍的) of rude behavior and 14 people in power, including professors, no longer 15 standards for 16 . That leads to a growing imprudence (轻率行为) 17 some college students. "There's a great 18 of bad behavior in the world around them, and young people see it and 19 disrespect," said Dr. Amanda, 20 that sometimes students "have no idea that they are being rude". | ||||
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