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1、卷号：（A）（年月日）机密学年第 2 学期2010 级计算机专业高等数学期中考试试卷A 卷题号一二三四五总分题分10 30 15 15 30 核分人得分复查人阅卷人一、选择题（本大题共5 小题，每小题2 分，共 10 分）1.下列方程所示曲面是双叶旋转双曲面的是()(A)1222zyx(B)zyx422(C)14222zyx(D)1164222zyx2.二元函数222214yxyxzarcsinln的定义域是()(A)4122yx(B)4122yx(C)4122yx(D)4122yx3.已知),(yxf在点),(00yx处连续,且两个偏导数),(00yxfx,),(00yxfy存在是),(yx
2、f在该点可微的()(A)充分条件,但不是必要条件;(B)必要条件,但不是充分条件;(C)充分必要条件;(D)既不是充分条件,也不是必要条件.4.下列直线中平行xOy坐标面的是 _（A）233211zyx；（B）04044zxyx；（C）10101zyx；（D）3221ztytx，5.函数zyxusinsinsin满足),(0002zyxzyx的条件极值是()(A)1;(B)0;(C)61;(D)81.二、填空题（本大题共10 个填空题，每空3 分，共 30 分）1.已知52|,|ba且,),(3ba则_)()(baba32.2.通过曲线0562222222yzxzyx,且母线平行于y轴的柱面方
3、程是_.3.若),ln(222zyxu则._du4.已 知 球 面 的 一 直 径 的 两 个 端 点 为532，和314，则 该 球 面 的 方 程 为_.5.函数2223uxyzz在点01,1,2M的梯度为 _及沿梯度方向上函数的方向导数为_.6设二元函数yxxyz32，则yxz2_7设0,00,),(2222222yxyxyxyxyxf,求),(yxfx=_.8.xyyxyx)2,1(),(lim=_.yxyyx)tan(lim)0,2(),(=_.三、解下列微分方程（本大题共3 小题，每小题5 分，共 15 分）1给定一阶微分方程dydx=3x（1）求它的通解；（2）求过点（2，5）的
4、特解；（3）求出与直线y=2x 1 相切的曲线方程。年级专业学号姓名装订线|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页，共 3 页2.解微分方程1)1(,)(ydyyxydx.3.求微分方程222xxexyy的通解.四、计算题（本大题共3 小题，每小题5 分，共 15 分）1方程组0022xuvyyvux所确定的隐函数的导数,xuxv.2设,sin,arctan,zf u vuxyvy f u v 可微，计算,zzxy.3vezusin，xyu,yxv,求yzxz,五、综合题（本大题共3 小题，每小题10 分，共 30 分）1.求点),
5、(341并与下面两直线531421yxzyxL:,tztytxL231422:都垂直的直线方程.2求曲线tztyttx3123cossincos在点),(132处的切线方程和法平面方程.3.求过直线0405zxzyx且与平面01284zyx组成4角的平面方程.2010-2011（2）计算机科学与技术专业高等数学期中考试试卷答案一、选择题（本大题共5 小题，每小题2 分，共 10 分）|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页，共 3 页文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3
6、E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 Z
7、Q8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3
8、E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 Z
9、Q8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3
10、E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 Z
11、Q8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3
12、E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L21.D.2.A.3.B.4.D 5.D.二、填空题（本大题共10 小题，每小题3 分，共 30 分）(1)141,(2)2222zx,(3)(zdzydyxdxzyx2222,(4)21113222zyx(5)2i-2j+k,3.(6)232xy；(7)0,00,22222223yxyxyxyxyxfx)(),(8)3/2,2.三、解下列微分方程（本大题共3 小题，每小题5 分，共 15 分）1.(1)y=32x2+C;(2)y=32x2-1;(3)y=3
13、2x2-13;2解:原方程可化为xyxyyxydxdy1-此方程为齐次方程令xyu,可将上述方程化为cxyxyxcxuudxxduuuuuudxdyxlnlnlnln11112将1)1(y代如上述方程,可得1c.故所求特解为1lnlnxyxyx.3.解:原方程为一阶线性微分方程,此时,22)(,2)(xxexqxxp.故由通解公式有).(22)(222)()(222cxecxdxecdxexeecdxexqeyxxxdxxxdxdxxpdxxp四、计算题（本大题共3 小题，每小题5 分，共 15 分）1解：uvxyuxxvxyuvvyuxu42422,22112cos,cos1fyfxy xf
14、xyy3)cos()sin(yxyxyexzxy)cos()sin(yxyxxeyzxy五、综合题（本大题共3 小题，每小题10 分，共 30 分）1.13464121zyxL:2切线方程:312322zyx,法平面方程:03322zyx3平面方程:0401272021zxzyx:,:.|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页，共 3 页文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP
15、1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L
16、2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP
17、1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L
18、2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP
19、1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L
20、2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2文档编码:CD3H3E1F3U8 HP1I8B1I4Z8 ZQ8I5N4L8L2