西南大学网络教育学院计算机数学基础17秋在线作业

欧阳老师

计算机数学基础


单项选择题
1、设A, B, C是三个事件，则A, B, C都不发生可表示为 .
    image/png;base64
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    D.?<imgsrc="data
单项选择题
2、空间直角坐标系中，与xOy坐标面距离为m(m &gt; 0)的平面方程为 .
    image/png;base64
    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"/>
    D.?<imgsrc="data
单项选择题
3、下列不定积分正确的是 .
    image/png;base64
    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"/>
    D.?<imgsrc="data
单项选择题
4、设f(x)的一个原函数为lnx，则 .
    image/png;base64
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    D.?<imgsrc="data
单项选择题
5、设z = x2 – 2y, 则= ( ).
    A.-2y
    B.-2
    C.2x
    D.2x-2y
单项选择题
6、下列级数中，发散的是 .
    image/png;base64
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    D.?<imgsrc="data
单项选择题
7、设函数，求= .
    image/png;base64
    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"/>
    D.?<imgsrc="data
单项选择题
8、设A与B是互逆事件，则下式中不成立的是 .
    image/png;base64
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    D.?<imgsrc="data
单项选择题
9、数列0, 1, 0, 1, 0, 1, …. .
    A.收敛于0
    B.收敛到1
    C.发散
    D.以上结论都不对
单项选择题
10、幂级数的收敛半径为 .
    A.1/2
    B.∞
    C.2
    D.1
单项选择题
11、微分方程的通解为 ，其中C为任意常数.
    image/png;base64
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    D.?<imgsrc="data
单项选择题
12、若，则 .
    image/png;base64
    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"/>
单项选择题
13、等比级数收敛到
    A.4
    B.3
    C.2
    D.1
单项选择题
14、微分方程的通解中有 个任意常数.
    A.0
    B.1
    C.2
    D.3
单项选择题
15、微分方程的通解为 .
    image/png;base64
    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"/>
    D.?<imgsrc="data
单项选择题
16、设f(x)是随机变量X的密度函数，则不正确的是 .
    image/png;base64
    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"/>
    D.?<imgsrc="data
单项选择题
17、要使函数在上连续，则= .
    A.0
    B.1
    C.-1
    D.2
单项选择题
18、已知随机变量X的密度函数，则D(X) = .
    A.1/3
    B.1/16
    C.1/4
    D.1/18
单项选择题
19、数列0, 1, 0, , 0, , 0, ,…. ,0, ,… .
    A.收敛于0
    B.收敛到1
    C.发散
    D.以上结论都不对
单项选择题
20、不定积分= .
    image/png;base64
    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"/>
    D.?<imgsrc="data
填空题
21、已知|q| &lt;1，则极限= .

填空题
22、微分方程的通解为 .

填空题
23、级数的通项un = .

填空题
24、球心在O(0, 0, 0)、半径为R的球面的方程为 .

填空题
25、设函数，则定积分 .

填空题
26、函数的定义域为 .

填空题
27、不定积分 .

填空题
28、设随机变量X ~ U[a, b]，则E(X)= .

填空题
29、5个球中有3个红球，2个白球，从中任取一球，则取到白球的概率为 .

填空题
30、设是连续函数，则a = .

填空题
31、 .

填空题
32、由参数方程所确定的函数的导数 .

填空题
33、微分方程的阶为 .

填空题
34、设, 则= .

填空题
35、抛物线在点A(1, 4)处的切线方程为 .

填空题
36、曲线在点(e, 2)处的切线方程是 .

填空题
37、方程表示的是 柱面.

填空题
38、已知, 则f(0) = .

填空题
39、函数的微分 .

填空题
40、已知，则dy = .

计算题
41、计算不定积分.

计算题
42、求极限.

计算题
43、曲线, 求在时对应曲线上点处的切线方程.

计算题
44、求积分

计算题
45、求函数的导数.

计算题
46、求由曲线及直线所围成的图形的面积.

计算题
47、求不定积分.

计算题
48、求极限

计算题
49、求函数的定义域.

计算题
50、设有点A(0, 0, 0)和B(1, 1, 2)，求线段AB的垂直平分面的方程.

计算题
51、设,求积分的值.

计算题
52、求极限.

计算题
53、计算.

计算题
54、求极限.

计算题
55、设，求.

证明题
56、求函数的极值.

证明题
57、判断级数是否收敛. 若级数收敛，试求其和.

证明题
58、已知，讨论a的取值.

证明题
59、讨论函数的极值

证明题
60、讨论的单调性和极值.
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