单选题 （共 6 题 ），每题只有一个选项正确
交换积分次序 $\int_{-1}^0 d y \int_{1-y}^2 f(x, y) d x=(\quad)$
$\text{A.}$ $\int_1^2 d x \int_0^{1-x} f(x, y) d y$
$\text{B.}$ $\int_1^2 d x \int_{1-x}^0 f(x, y) d y$
$\text{C.}$ $\int_0^2 d x \int_0^{1-x} f(x, y) d y$
$\text{D.}$ $\int_0^2 d y \int_{1-x}^0 f(x, y) d x$
下列级数中绝对收敛的是 ( )。
$\text{A.}$ $\sum_1^{\infty} \frac{(-1)^n}{\ln (1+n)}$
$\text{B.}$ $\sum_1^{\infty} \frac{n^3-1}{n^2+2}$
$\text{C.}$ $\sum_1^{\infty}(-1)^n \frac{2 n^2+1}{n^3-2 n+1}$
$\text{D.}$ $\sum_1^{\infty} \frac{(-1)^n n}{\sqrt{3^n}} \sin n$
设 $z=x^y$, 则有
$\text{A.}$ $\frac{\partial z}{\partial x}=x^y \ln x$
$\text{B.}$ $\frac{\partial z}{\partial x}=y x^{j-1} d x$
$\text{C.}$ $\frac{\partial z}{\partial x}=x^y$
$\text{D.}$ $\frac{\partial z}{\partial x}=y x^{j-1}$
若 $\sum_{n=1}^{\infty} a_n(x-1)^n$ 在 $x=-1$ 处收敛, 那么当 $x =2$ 时该级数 $(\quad)$
$\text{A.}$ 条件收敛
$\text{B.}$ 绝对收敛
$\text{C.}$ 发散
$\text{D.}$ 敛散性不变
已知平面区域 $D_1=\left\{(x, y) \left\lvert\, 0 \leqslant y \leqslant x \leqslant \frac{\pi}{2}\right.\right\}, D_2=\left\{(x, y) \left\lvert\, 0 \leqslant x \leqslant y \leqslant \frac{\pi}{2}\right.\right\}$, $D_3=\left\{(x, y) \left\lvert\, \frac{\pi}{2} \leqslant x \leqslant y \leqslant \pi\right.\right\}$, 记 $I_1=\iint_{D_1} e ^{-x^2} \sin y d x d y, I_2=\iint_{D_2} e ^{-x^2} \sin y d x d y, I_3=\iint_{D_3} e ^{-x^2} \sin y d x d y$,则（）
$\text{A.}$ $I_3 < I_1 < I_2$.
$\text{B.}$ $I_3 < I_2 < I_1$.
$\text{C.}$ $I_1 < I_3 < I_2$.
$\text{D.}$ $I_1 < I_2 < I_3$.
(2) $\int_{-1}^0 d x \int_{-x}^{\sqrt{2-x^2}} f(x, y) d y+\int_0^1 d x \int_x^{\sqrt{2-x^2}} f(x, y) d y=(\quad)$
$\text{A.}$ $\int_0^1 d y \int_{-y}^y f(x, y) d x+\int_1^2 d y \int_{-\sqrt{2-y^2}}^{\sqrt{2-y^2}} f(x, y) d x$
$\text{B.}$ $\int_0^1 d y \int_{-y}^y f(x, y) d x+\int_1^{\sqrt{2}} d y \int_{-\sqrt{2-y^2}}^{\sqrt{2-y^2}} f(x, y) d x$
$\text{C.}$ $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} d \theta \int_0^2 f(r \cos \theta, r \sin \theta) r d r$
$\text{D.}$ $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} d \theta \int_0^{\sqrt{2}} f(r \cos \theta, r \sin \theta) d r$