中国石油大学2019高等数学高数期末考试试卷及答案

2019—2020专业班级开课系室考试日期页号阅卷人5一.共44分)zxy),则3dxdyy22．12f(x,xdx1dy1f(x,y)xysinxy则=0y1cosxx,0xf(x)21,x0()sx()fxx以21s().2（xy—3ds22xyR222R3CC44=x3y2z02xy10z30,L为L平行于平面L垂直于平面为4x2yz20（C）.L上与Lyzx222:xyzR2222（BR4R433R4R4C.n(n((n)nnn1n1n1n11)n3ennnnn1n1an设n1D）aa2aaannnnn1若n1n1n1n1alim1aan1aSnnnn1n1nn88uy,xy)y.uf(xf2u2fx122u22xy(xff)(xff)22y12xf2xyf(2xyx)ff321z3xyxyyx122轴x.1xxL:02)Tyx21处的切向量T2)5，12cos,cos55zxz|y||(6xy|132y2)2)2)(1,2)T2)z|2555T(1,2)(xy),2Dx,y)xy.22D2(xydxdy(xy)dxdy222解Dx2y24x2y242d2r3dr000=)zxyz11xy2222..已知,y,zxyo0K(x,y,z)k|z|0：040r2cos法1：(x,y,z)dxdydzk|z|dxdydzcossindrdd2cosrr24k000k6=D:xyy022xyz11xy2222法2：M(x,y,z)dxdydzk|z|dxdydz211rkddr100rk6=kMk|z|dxdydzzzdzz(zdz1222601法3：(xy)(yx)Ix2y2y1x22CC(xy)(yx)I1CQP(dxdyxyx2y21(]dxdyx2y21xyzdydzxydxdzzx2dxdyyz1x222xyzdydzxydxdz(zx2)dxdy(yzxxdxdydz2(xx210(xyzdxdydz22231342ddr140001xnn1n1R1，收敛域为[1xxnxS(x)xn1xnxx0n100n1=n1n1xxx)x1x0x0S(0)0x)x[(xS(x)x0x04eyexdxdyD{(x,y)|xy22D.eexyxdxdydxdyyxeeyDDe1eeyxxydxdy（dxdydxdy）ex2eeyDDD1ee1yx(2ee2xy=D8xoyD{(x,y):xM(x,y)yxyh(x,y)75xyh(x,y)xy.22220D0g(x,y)g(x,y)0000xy75g(x,y)x2y2DM(x,y)h(x,y)处00(x,y)(y2x)i(x2y)j000000g(x,y)(x,y)(y2x)(x2y)22000000005x5y8xy.202000f(x,y)g(x,y)5x5y8xy222(,)558fxyx2y20x2y2xy)LagrangeL(x,y)5x5y8xy(75xy2222做108(2)xyyxLx108(2)0,(2)yxxyLy750.xyLx2y22)式相加可得(xy)(2)yx,或2.若yx,x53,y53.yxxy