### 1995年全国硕士研究生招生统一考试数学试题及详细参考解答(数一)

$\text{A.}$ 平行于 $\pi$. $\text{B.}$ 在 $\pi$ 上. $\text{C.}$ 垂直于 $\pi$. $\text{D.}$ 与 $\pi$ 斜交.

$\text{A.}$ $f^{\prime}(1)>f^{\prime}(0)>f(1)-f(0)$. $\text{B.}$ $f^{\prime}(1)>f(1)-f(0)>f^{\prime}(0)$. $\text{C.}$ $f(1)-f(0)>f^{\prime}(1)>f^{\prime}(0)$. $\text{D.}$ $f^{\prime}(1)>f(0)-f(1)>f^{\prime}(0)$.

$\text{A.}$ 充分必要条件. $\text{B.}$ 充分条件但非必要条件. $\text{C.}$ 必要条件但非充分条件. $\text{D.}$ 既非充分条件又非必要条件.

$\text{A.}$ $\sum_{n=1}^{\infty} u_{n}$ 与 $\sum_{n=1}^{\infty} u_{n}^{2}$ 都收敛. $\text{B.}$ $\sum_{n=1}^{\infty} u_{n}$ 与 $\sum_{n=1}^{\infty} u_{n}^{2}$ 都发散. $\text{C.}$ $\sum_{n=1}^{\infty} u_{n}$ 收敛而 $\sum_{n=1}^{\infty} u_{n}^{2}$ 发散. $\text{D.}$ $\sum_{n=1}^{\infty} u_{n}$ 发散而 $\sum_{n=1}^{\infty} u_{n}^{2}$ 收敛.

$$\boldsymbol{A}=\left(\begin{array}{lll} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array}\right), \quad \boldsymbol{B}=\left(\begin{array}{ccc} a_{21} & a_{22} & a_{23} \\ a_{11} & a_{12} & a_{13} \\ a_{31}+a_{11} & a_{32}+a_{12} & a_{33}+a_{13} \end{array}\right),$$
$$\boldsymbol{P}_{1}=\left(\begin{array}{lll} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right), \quad \boldsymbol{P}_{2}=\left(\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{array}\right),$$

$\text{A.}$ $\boldsymbol{A} \boldsymbol{P}_{2} \boldsymbol{P}_{1}=\boldsymbol{B}$. $\text{B.}$ $\boldsymbol{A P} \boldsymbol{P}_{1}=\boldsymbol{B}$. $\text{C.}$ $\boldsymbol{P}_{2} \boldsymbol{P}_{1} \boldsymbol{A}=\boldsymbol{B}$. $\text{D.}$ $\boldsymbol{P}_{1} \boldsymbol{P}_{2} \boldsymbol{A}=\boldsymbol{B}$.

$\lim _{x \rightarrow 0}(1+3 x)^{\frac{2}{\sin x}}=$

$\frac{\mathrm{d}}{\mathrm{d} x} \int_{x^{2}}^{0} x \cos \left(t^{2}\right) \mathrm{d} t=$

\begin{aligned} & P\{X \geq 0, Y \geq 0\}=\frac{3}{7}, \quad P\{X \geq 0\}=P\{Y \geq 0\}=\frac{4}{7}, \\ & \text { 则 } P\{\max (X, Y) \geq 0\}= \end{aligned}

$$\int_{(0,0)}^{(t, 1)} 2 x y \mathrm{~d} x+Q(x, y) \mathrm{d} y=\int_{(0,0)}^{(1, t)} 2 x y \mathrm{~d} x+Q(x, y) \mathrm{d} y,$$

(1) 在开区间 $(a, b)$ 内 $g(x) \neq 0$;
(2) 在开区间 $(a, b)$ 内至少存在一点 $\xi$, 使 $\frac{f(\xi)}{g(\xi)}=\frac{f^{\prime \prime}(\xi)}{g^{\prime \prime}(\xi)}$.

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