分析

简答题:设DR2是有界单连通闭区域,

取得最大值的积分区域记为D1
(Ⅰ)求I(D1)的值;
(Ⅱ)

其中D1是D1的正向边界.

正确答案
(Ⅰ)要使取得最大值,则D应该包含所有使得被积函数f(x,y)=4-x2-y2≥0并且D中不能包含使得f(x,y)=4-x2-y2<0的区域,故D1={(x,y)x2+y2≤4},

又Q(x,y),P(x,y)在D1围成的区域D1上有奇点,所以要补充曲线L:x2+4y22,ε>0足够小,取顺时针方向,且L围成的区域为D”,则Q(x,y),P(x,y)在D1与L围成的区域D’上满足格林公式的条件,
查看解析

相关试题

单选
A 连续且取得极大值 B 连续且取得极小值 C 可导且导数为零 D 可导且导数不为零
查看
单选
设函数f(x,y)可微,且f(x+1,ex)=x(x+1)2,f(x,x2)=2x2lnx,则df(1,1)=(  ).
A dx+dy B dx-dy C dy D -dy
查看
单选
设函数处的3次泰勒多项式为ax+bx2+cx3,则(  ).
A a=1,b=0,c=-<img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232738_7101.gif" /> B a=1,b=0,c=<img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232738_7101.gif" /> C a=-1,b=-1,c=-<img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232738_7101.gif" /> D a=-1,b=-1,c=<img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232738_7101.gif" />
查看
单选
设函数f(x)在区间[0,1]上连续,则(  ).
A <img width="168" height="46" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232740_8350.jpg" /> B <img width="168" height="46" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232742_3830.jpg" /> C <img width="157" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232743_0705.jpg" /> D <img width="132" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232744_6319.jpg" />
查看
单选
二次型f(x1,x2,x3)=(x1+x2)2+(x2+x3)2-(x3-x1)2的正惯性指数与负惯性指数依次为(  ).
A 2,0 B 1,1 C 2,1 D 1,2
查看
单选
β2,β3两两相交,则l1,l2依次为().
A <img width="51" height="40" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232746_7725.jpg" /> B <img width="70" height="40" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232747_3663.jpg" /> C <img width="78" height="40" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232748_9913.jpg" /> D <img width="96" height="40" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232749_5226.jpg" />
查看
单选
设A,B为n阶实矩阵,下列结论不成立的是(  ).
A <img width="177" height="53" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232751_1320.jpg" /> B <img width="167" height="53" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232751_6632.jpg" /> C <img width="181" height="53" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232753_2726.jpg" /> D <img src="https://www.beizhujiaoyu.com/uploads/202208/165234134072341.jpg" alt="" />
查看
单选
设A,B为随机事件,且0
A 若P(A|B)=P(A),则P(A|<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232635_4445.gif" />)=P(A) B 若P(A|B)>P(A),则P(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />|<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232635_4445.gif" />)>P(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />) C 若P(A|B)>P(A|<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232635_4445.gif" />),则P(A|B)>P(A) D 若P(A|A<img width="26" height="20" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232755_4132.gif" />B)>P(<img width="24" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232633_0382.gif" />|A<img width="26" height="20" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232755_4132.gif" />B),则P(A)>P(B)
查看
单选
设(X1,Y1),(X2,Y2),…,(Xn,Yn)为来自总体的简单随机样本,令=,则(  ).
A <img width="322" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232759_7256.jpg" /> B <img width="342" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232800_1319.jpg" /> C <img width="411" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232801_8663.jpg" /> D <img width="432" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232802_2725.jpg" />
查看
单选
设X1,X2,…,X16是来自总体N(μ,4)的简单随机样本,考虑假设检验问题:H0:μ≤10,H1:μ>10.(x)表示标准正态分布函数.若该检验问题的拒绝域
A 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(0.5) B 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(1) C 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(1.5) D 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(2)
查看
刷题小程序
数学一题库小程序