《高数B第二学期综合复习题 答案.docx》由会员分享,可在线阅读,更多相关《高数B第二学期综合复习题 答案.docx(2页珍藏版)》请在第一文库网上搜索。
1、高等数学B (综合测试答案)一、填空题(每题3分,共30分)1. 1 .2. _y/133. -5 .4. sin(yz)d+xz cos(yz) + xy cos(yz)dz .5. 0.6. y = -2e2x.7. y = c,1(y1-y2) + c2(y2-3) + y1.8. x+y + z-y-4 = 0.911 + + (-)2 + +)+ ,-2xyIa-b,a-b,U z . z 1 故 ciF b = Ix y解: = 2y- = (6xy2+6x3y5)exxxy解:特征方程为:r2-3r + 2 = 0特征根为:4=2,0=1对应齐次方程的通解是:y = cle2r
2、+ c2ev设原方程的特解为:y=axex,将其代入原方程待定系数得4 = -2.所以y = -2xex故原方程的通解为y = c12x + CE-2xev由 y(0) = 0,y(0) = 1 解得q =3,C2= -3因此所求的特解是y = 3e2x -3ex -2xex六、解:(x2 + y)dxdy = x1dxdy =d(rcos0)2rdr =654七、解:的方程是Z = +y2(0z2). JJ( + r Mp =呵。丽J; P2dz 2P3(2-P2 )dp =,八、解.:收敛半径H = 2,收敛区间为一1,3)s(x) = Y(-rnTs(x) = QSN M=I(-l,4-
3、5(1) = O ,=l5(x) = ln 2-ln(3-x)(-lx3)九、解:方程/(x)COSX+ 2,/Sinr力=x +1两边对X求导得f,(x) cos X + f(x) sin X = 1即 ,(x) + tanx(x)=COSX求解上面的一阶线性微分方程得f(x) = e Jtan”, F !Jan wN + C = sinx + Ccos xj COSX由于/(0) = l,所以 C = I,故/(无)= sinX+ cosX十、解:设尸(x,y,z) = l + V + y2-z,得工=2x,g=2y,优=T抛物线在(Xo,%,Zo)处的切平面方程为 2x0(x-) + 2y0(y- y0) -(z-zo) = O即z = 2xqx + 2yQy +1 -片- y;该平面与抛物面及圆柱面所围成的立体的体积为V = d rdr、 dz =+ y)-.-2xnJOJ2jrcos+2)rsin+l-y02=2;TXo 2, = 0商 0 n= 2yo=O双得Xo = Lyo =0,由提意可知V的最小值一定存在,且只有一个驻点,故可断定V的最小值为3冗V = + -2-,切平面为z = 2x 22