2022年全国硕士研究生入学统一考试数学(二)模拟题二

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A 高阶无穷小 B 低阶无穷小 C 同阶非等价无穷小 D 等价无穷小

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A x=0必是g(x)的第一类间断点 B x=0必是g(x)的第二类间断点 C x=0必是g(x)的连续点 D g(x)在点x=0处的连续性与a的取值有关

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于( )．

A 1 B -1 C <img width="19" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20211027071902_5406.jpg" /> D <img width="39" height="37" src="https://www.beizhujiaoyu.com/uploads/202208/20211027071903_1499.jpg" />

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A <img src="https://www.beizhujiaoyu.com/uploads/202208/162823953550751.png" width="94" height="32" /> B <img src="https://www.beizhujiaoyu.com/uploads/202208/162823953913531.png" width="94" height="31" /> C <img src="https://www.beizhujiaoyu.com/uploads/202208/162823954389511.png" width="76" height="31" /> D <img src="https://www.beizhujiaoyu.com/uploads/202208/162823954953091.png" width="89" height="32" />

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设函数f(x)可导，y=f(x3)，当自变量x在x=-1处取得增量△x=-0.1时，相应的函数增量△y的线性主部为0.3，则f'(-1)=( )．

A -1 B 0.1 C 1 D 0.3

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用铁锤将一铁钉打击入木板，设木板对铁钉的阻力与铁钉击人木板的深度成正比．在铁锤击第一次时能把铁钉击入1 cm，如果铁锤每次打击做的功相等，则第二次能把铁钉击入_

A <img width="38" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210928231850_8507.gif" />+1． B <img width="56" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210928231933_2567.gif" /> C <img width="38" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210928231850_8507.gif" />-1． D <img width="38" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210928231850_8507.gif" />-<img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210928224426_3250.gif" />．

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对二元函数z=f(x，y)，下列结论正确的是( )．

A z=f(x，y)可微的充分必要条件是z=f(x，y)有一阶连续的偏导数 B 若z=f(x，y)可微，则z=f(x，y)的偏导数连续 C 若z=f(x，y)偏导数连续，则z=f(x，y)一定可微 D 若z=f(x，y)的偏导数不连续，则z=f(x，y)一定不可微

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设A是m×s矩阵，B是s×n矩阵，则齐次线性方程组Bx=0和ABx=0是同解方程组的一个充分条件是( )．

A r(A)=m B r(A)=s C r(B)=s D r(B)=n

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A <img src="https://www.beizhujiaoyu.com/uploads/202208/162885840525401.png" width="134" height="73" /> B <img src="https://www.beizhujiaoyu.com/uploads/202208/162885840956201.png" width="150" height="72" /> C <img src="https://www.beizhujiaoyu.com/uploads/202208/162885841343831.png" width="168" height="113" /> D <img src="https://www.beizhujiaoyu.com/uploads/202208/162885842019981.png" width="134" height="72" />

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二次型f(x1，x2，x3)=(x1-x2)2+(x2-x3)2+(x3-x1)2的标准形为（）．

A <img src="https://www.beizhujiaoyu.com/uploads/202208/16288590327641.png" width="128" height="17" /> B <img src="https://www.beizhujiaoyu.com/uploads/202208/162885903622671.png" width="116" height="31" /> C <img src="https://www.beizhujiaoyu.com/uploads/202208/162885904287831.png" width="128" height="17" /> D <img src="https://www.beizhujiaoyu.com/uploads/202208/162885904713141.png" width="154" height="31" />

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