问题 填空题

函数f(x)=loga(x-1)+1(a>0且a≠1)的图象恒过点A,若点A在直线mx-y+n=0上,则4m+2n的最小值为______.

答案

由题意,函数f(x)的图象恒过(2,1)即A(2,1),故2m+n=1.

∴4m+2n≥2

4m2n
=2
22m+n
=2
2

当且仅当4m=2n,即2m=n,

即n=

1
2
,m=
1
4
时取等号.

∴4m+2n的最小值为2

2

故答案为:2

2

完形填空
完形填空。
     Many people think the  1  time is spent, the more work will be done. So students have to spend the
whole day doing school work  2  the three meals.
     Modern students have many  3 . They love sports, computers and music. A  4  holiday can get them
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weekend homework. So they don't do it  6  Sunday night. And there is not enough time to finish the
homework carefully. The poor weekend homework usually makes teachers  7 .
     Things always get worse  8  right ideas. Too much school work makes students lose  9  in learning.
It's also bad for their health.
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should be  10  to give students both pleasure and knowledge.
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判断题