下列命题中，真命题是（） A．存在x∈R，sin2x2+cos2x2=12 B．任_爱下问搜题

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问题选择题

下列命题中，真命题是（　　）

A．存在x∈R，sin2

x

2

+cos2

x

2

=

1

2

B．任意x∈（0，π），sinx＞cosx

C．任意x∈（0，+∞），e^x＞1+x

D．存在x∈R，x²+x=-1

答案

根据同角基本关系可知，sin2

x

2

+cos2

x

2

=1恒成立，故A错误

例如x=

π

6

∈(0，π)，但是sinx＜cosx，故B错误

令f（x）=e^x-x-1，x＞0，则f′（x）=e^x-1＞0，x∈（0，+∞）

∴f（x）在x∈（0，+∞）单调递增，

∴f（x）＞f（0）=0，即e^x＞1+x，故C正确

由于x²+x+1=(x+

1

2

)2+

3

4

＞0恒成立，故x²+x=-1不可能成立，故D错误

故选C

完形填空

阅读下面短文，掌握其大意，从下列各各题所给的四个选项（A 、B、C和D）中，选出最佳选项，并在答题卷上将该项涂黑。
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B．misunderstood

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D．overflowing

判断题

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