zxy122(2,1,4)(C)杭州電子科技大學(xué)信息工程學(xué)院學(xué)生考試卷（期末）A卷x2y1z4x2y1z4；；421421課程名稱考生姓名學(xué)號(hào)高等數(shù)學(xué)（下）考試日期時(shí)間共120分鐘xy(z0；任課教師姓名:xyzRdS班級(jí)專業(yè)2222（D）四R2R20R22sin一、填空題(每小題3分，共計(jì)15分)（A）nnn11．點(diǎn)(4,x34到坐標(biāo)軸的距離為.A9xyz2222280在xoyxy22x.三、試解下列各題（每小題6分，共計(jì)12分）z1xz0(1,0,1)ab和.)zsin(xy)dzcos(xy)(xdy).ijkn211(1,1,3)1:(1)n1:.110nn1xy3z4)[,)f(x)x.5．f(x)設(shè)2x0.二、單項(xiàng)選擇題（每小題3分，共計(jì)15分）zzarctan(xy)(B)rr2rxyz,x222求.xx2yyyysec2(xy)rx1xy1xy1xy222222:))xrzxy3x3y9x3322）(B)ryz222x2r3zzzz第1頁共3頁四、試解下列各題（每小題6分，共計(jì)36分）nxn1xzzzzzz(x,y)ln、設(shè).n1yxyx(1,1)分F(x,y,z)zy:令))))zxnxn111z2(xz)yn分F,F,Fn1n1zxyzxzxFzn分xFxzn1zxzFz2分1xyF(xz)y1zx(分t1t(1x)2x,y,zt2t12..1tt0xdsyxyx2.L分1Lt1(2:=()0Lyxyx2111112114dx2分xdxxxT(,,2t)(,1,2)=)(1t)t440022t111213x(14x)222分120120x2z12y,))14821(551)分2122x8y16z12(xy)(xy)2yxx6.L2LIxydD:.,Qxsiny分Dyx,yxPxy:2D2.解令QP1,1Iyydyxdx:)分y2xyxyy1391(yy)dyxy2))220x到(1,0)1分y沿201(1sin)ydy6xyx()()1yxdx2=2x00L53圖1)........................................................................................6分第2頁共3頁試解下列各題（8分）5xy0x2y0及1xoy.nn1x2y162(x,y)zxy分225設(shè)ss分nnz2n12x(2xy0xz54ss,sn()s分分11由分n2nss0(n)2n5yn811xss2n2但分5165n1n22nn,..............................................................................7分yss0(n)分故2nn18(,)故9.55nn1hIzdxdydz:zxy2Rhzh(2與.RIzdxdyxyzR2.222R2hzdz2分I:h20Rh2分=24Izdxd