### 1991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(数二)

$\text{A.}$ $a=0, b=-2$ $\text{B.}$ $a=1, b=-3$ $\text{C.}$ $a=-3, b=1$ $\text{D.}$ $a=-1, b=-1$

$\text{A.}$ $F(x)=\left\{\begin{array}{cl}\frac{x^3}{3}, & 0 \leq x \leq 1 \\ \frac{1}{3}+2 x-\frac{x^2}{2}, & 1 < x \leq 2\end{array}\right.$ $\text{B.}$ $F(x)=\left\{\begin{array}{cc}\frac{x^3}{3}, & 0 \leq x \leq 1 \\ -\frac{7}{6}+2 x-\frac{x^2}{2}, 1 < x \leq 2\end{array}\right.$ $\text{C.}$ $F(x)=\left\{\begin{array}{cr}\frac{x^3}{3}, & 0 \leq x \leq 1 \\ \frac{x^3}{3}+2 x-\frac{x^2}{2}, 1 < x \leq 2\end{array}\right.$ $\text{D.}$ $F(x)=\left\{\begin{array}{c}\frac{x^3}{3}, \quad 0 \leq x \leq 1 \\ 2 x-\frac{x^2}{2}, 1 < x \leq 2\end{array}\right.$

$\text{A.}$ $x_0$ 必是 $f(x)$ 的驻点 $\text{B.}$ $-x_0$ 必是 $-f(-x)$ 的极小值点 $\text{C.}$ $-x_0$ 必是 $-f(x)$ 的极小值点 $\text{D.}$ 对一切 $x$ ，都有 $f(x) \leq f\left(x_0\right)$

$\text{A.}$ 没有渐近线 $\text{B.}$ 仅有水平渐近线 $\text{C.}$ 仅有铅直渐近线 $\text{D.}$ 既有水平渐近线又有铅直渐近线

$\text{A.}$ $\int_{-l}^0 \frac{k m \mu \mathrm{d} x}{(a-x)^2}$ $\text{B.}$ $\int_0^l \frac{k m \mu \mathrm{d} x}{(a-x)^2}$ $\text{C.}$ $2 \int_{-\frac{l}{2}}^0 \frac{k m \mu \mathrm{d} x}{(a+x)^2}$ $\text{D.}$ $2 \int_0^{\frac{l}{2}} \frac{k m \mu \mathrm{d} x}{(a+x)^2}$

$\int_1^{+\infty} \frac{\ln x}{x^2} \mathrm{~d} x=$

$\lim _{x \rightarrow 0^{+}} \frac{1-e^{\frac{1}{x}}}{x+e^{\frac{1}{x}}}=$

$$|A B|:|D C|=2: 1,|A B| < 1,$$

$$f(x)=f(x-\pi)+\sin x .$$

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