2012高数下期中答案new

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1、s[6UCCk.C(92011—2012h'$+m2"
m;XVDDl/D(AV)(A"11F7F4)#2(e3.,815.)1.(,*/=Z=f(x,y),`*;i-w.;:5x
(B).(A)i℄,3w.1(B)i℄,3w.1(C)w.1,3i℄(D)w.1,)i#&12.222vf2x+3y+z=91%P(1,−1,2)qjf-(C).(A)2x+3y+2z=9(B)2x-3y+2z=4(C)2x-3y+2z=9(D)2x+3y-2z=4RπR143.~f(x,y)℄=,3dθf

2、(rcosθ,rsinθ)rdr!,(C).00√√√√Z2Z1−x2Z2Z1−x222(A)dxf(x,y)dy(B)dxf(x,y)dy000x√√√√Z2Z1−y2Z2Z1−y222(C)dyf(x,y)dx(D)dyf(x,y)dx0y00!π54.~u.D)vy=sinx,x=±2Cy=1.3(xy−1)dxdy(D).D(A)π(B)2(C)−2(D)−π5.x~y=e(C1sinx+C2cosx)(C1,C2z&)g*p.-Æ,31-(B).′′′′′′′′′′′(A)y+2y+y=0(B)y−2y+y=0(C)y−2y=0(D)y+y=0*

3、Y(e3.,815.)√1.%(2,1,0)jf3x+4y+5z=0TZd=2.√√2.◦~a=~b=3,~a−~b=_~a-~b9Hϕ=135,r2,317.3.x~z=(x+2y),31%(1,0)wR.dzR=dx+2dy.RRaxaa4.~f(x,y)℄=,3A.:dxf(x,y)dy=dyf(x,y)dx.000y1∂z∂z5.2~Z=f(lnx+y),o:=f(u)W.3x∂x+y∂y=0.G}(e7.,814.)84!#1!s[6UCCk.C(9∂2w1.~w=f(x+y+z,xyz),o:fS*3*℄i,t.∂x∂zF

4、:au=x+y+z,v=xyz,35R0?=t,3,*∂w∂f∂u∂f∂v=·+·=f′+yzf′,........................2∂x∂u∂x∂v∂x12.∂2w∂∂f′∂f′=(f′+yzf′)=1+yf′+yz2,..................4∂x∂z∂z12∂z2∂z.′′?&f1>f2{
0?=,:*∂f′∂f′∂f′11∂u1∂v′′′′=·+·=f+xyf,........................5.∂z∂u∂z∂v∂z1112∂f′∂f′∂f′22∂u2∂v′′′′=·+·=f+xyf,........................6

5、.∂z∂u∂z∂v∂z2122∂2w′′′′′′′′′=f+xyf+yf+yz[f+xyf]∂x∂z111222122′′′′2′′′=f+y(x+z)f+xyzf+yf...........................7.1112222!2.222Gy[1+x(x+y)]dxdy,o:A.u.D)vy=x-y=1.D22F:~g(x,!y)=xy(x+y),),D;,y>(Æ,rg(−x,y)=−g(x,y),:)*

6、y[1+x(x+y)]dxdy=ydxdy=dxydy−1x2DDZ1144=(1−x)dx=.............................7.2−15(8.)~#jf<^%M1(1,1,1),M2(0,1,−1),r-jfx+y+z=07,tjf-.−−−−→F:~tjf,_~n=(A,B,C).)W6~n-M1M2=(−1,0,−2)7,:*−A−2C=0......................................2.+'tjf-$6jfx+y+z=07,+*A+B+C=0...............................

7、......4.)*A=−2C,B=C......................................6.84!#2!s[6UCCk.C(9)jf%,-W6tjf-A(x−1)+B(y−1)+C(z−1)=0.Etjf-2#x−y−z=0....................................................8.222(