问题 问答题

求常数k的取值范围,使得不等式kln(1+x)>arctanx当x>0时成立.

答案

参考答案:从题设可知只需考察k>0的情形.
设f(x)=kln(1+x)-arctanx,则f(0)=0,且
[*]
令g(x)=kx2-x+k-1,则当x>0时f’(x)与g(x)同号.
由于g(x)满足
[*]
由此可见g(x)在(0,+m)上的最小值[*].
为使[*]必须且只需正数k满足[*]>[*].即使得不等式kln(1+x)>arctanx当x>0时成立的k是大于[*]+1)的一切正数.

改错题

第二卷(共35分)

第三部分:写作(共两节,满分35分)                         

第一节  短文改错(共10小题;每小题1分,满分10分)

此题要求改正所给短文中的错误。对标有题号的每一行作出判断:如无错误,在该行右边横线上画一个勾(√);如有错误(每行只有一个错误),则按下列情况改正:

此行多一个词:把多余的词用斜线(\)划掉,在该行右边横线上写出该次,并也用斜线划掉。

此行缺一个词:在缺词处加一个漏字符号(∧),在该行右边横线上写出该加的词。

此行错一个词:在错的词下划一横线,在该行右边横线上写出改正后的词。

注意:原行没有错的不要改。

Dear Sir,

I am now a college student in Peking University. I' m      76. __________

quite interested in the position offering by your website     77. __________

for part-time English reporters. I think I' m fit the job.          78. ___________

As a student, I've read a lot and have many knowledge in        79. ___________

different field. I' m fond of English and do well in both     80. ___________

speaking and writing. Besides, I'm easily to get along      81. ___________

with and I enjoy working together with another. Above         82. ____________

all, I once work as a reporter for my college broadcast          83. ___________

station. So I' m sure I can do the job well if I will get          84. ___________

the chance to work for a website. I'm looking forward          85. ___________

to your reply.

Yours faithfully,

Li Hua

单项选择题 B1型题