2019年全国硕士研究生招生考试《数学一》真题及解析

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当x→0时，x-tanx与xk是同阶无穷小，则k=( )．

A 1 B 2 C 3 D 4

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A 可导点，极值点 B 不可导点，极值点 C 可导点，非极值点 D 不可导点，非极值点

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设{un}是单调增加的有界数列，则下列级数中收敛的是( )．

A <img width="44" height="37" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232617_5851.jpg" /> B <img width="108" height="44" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232619_5539.jpg" /> C <img width="113" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232619_7570.jpg" /> D <img width="121" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232621_7882.jpg" />

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，如果对上半平面(y>O)内的任意有向光滑封闭曲线C都有Q(x，y)dy=0，那么函数P(x，y)可取为( )．

A <img width="51" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232624_2101.jpg" /> B <img width="61" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232626_1476.jpg" /> C <img width="62" height="43" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232626_4132.jpg" /> D <img width="51" height="44" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232628_3351.jpg" />

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设A是三阶实对称矩阵，E是三阶单位矩阵，若A2+A=2E，且|A|=4，则二次型xTAx的规范形为( )．

A <img width="122" height="38" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232628_6164.gif" /> B <img width="116" height="38" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232630_4757.gif" /> C <img width="108" height="38" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232630_8820.gif" /> D <img width="120" height="38" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232632_6164.gif" />

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如图所示，有3张平面两两相交，交线相互平行，它们的方程ai1x+ai2y+ai3z=di(i=1，2，3)组成的线性方程组的系数矩阵和增广矩阵分别记为A，，则(

A r(A)=2，r(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />)=3 B r(A)=2，r(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />)=2 C r(A)=1，r(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />)=2 D r(A)=1，r(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />)=1

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设A，B为随机事件，则P(A)=P(B)的充分必要条件是( )．

A P(A∪B)=P(A)+P(B) B P(AB)=P(A)P(B) C P(A<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232635_4445.gif" />)=P(B<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />) D P(AB)=P(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" /><img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232635_4445.gif" />)

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设随机变量X和Y相互独立，且都服从正态分布N(μ，σ2)，则P{|X-Y|

A 与μ无关，而与σ2有关 B 与μ有关，而与σ2无关 C 与μ，σ2都有关 D 与μ，σ2都无关

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填空题:设函数f(u)可导，z=f(siny-sinx)+xy，则

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填空题:微分方程2yy’-y2-2=0满足条件y(0)=1的特解为______．

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