2011-2012-2高数下a卷答案

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1、#jA!9e_}9_℄CW2011—2012:x/*4:=(:I
,hfÆ`~:Æ`(Af)(^=11kB?)>8(s239,D159)1.xy=C1e+(C2cosx+C3sinx)(C1,C2,C3'A)'vÆ[*/5%97'$,<7'(D).′′′′′′′′′′′′(A)y+y−y−y=0(B)y+y+y+y=0′′′′′′′′′′′′(C)y−y−y+y=0(D)y−y+y−y=0√2.

2、~a

3、=4,

4、~b

5、=2,~a·~b=42,

6、~a×~b

7、=(C)

8、.√√2√(A)22(B)(C)42(D)223.3Gz=f(x,y)+P0(x0,y0)fx(x0,y0),fy(x0,y0)G<+g%9'(A).(A);#W289#W(B)9#W28;#W(C)S89F8;#W(D)9;#W!4.π5
DD/y=sinx,x=±2y=1&.(xy−1)dxdy'(B).D(A)π(B)−π(C)−2(D)2P∞P∞5.unmGs,(un+un+1)mG(A).n=1n=1(A)2s−u1(B)2s+u1(C)2s(D)2s+2u1

9、3"i(s239,D159)x−1yz+3xy+2zπ1.U/L1:==HL2:=='TZ'.1−412−2−14rx2.2f(x,y)=xy+(y−1)arcsiny,fx(x,1)=1.3.22uz=x+yH

10、u2x+4y−z=0

11、4'

12、u72x+4y-z=5.RR√RR1x1y4.f(x,y)'l7G,Y96:dxf(x,y)dy=dyf(x,y)dx.0x0y2Hds√5.L+A(1,0),B(0,1),C(−1,0),D(0,−1)',+'R73℄,=42.

13、x

14、+

15、y

16、Ld

17、5f1f#jA!9e_}9_℄CWÆR(s279,D149)∂2z1.22z=f(x−y,2xy),
XfdE>3[l7{$,∂x∂y.22e:pu=x−y,v=2xy,;
G$6,E∂z∂f∂u∂f∂v′′=·+·=2xf+2yf,.........................29∂x∂u∂x∂v∂x12∂2z∂∂f′∂f′=(2xf′+2yf′)=2x1+2f′+2y2,..................4∂x∂y∂y12∂y2∂y9′′A%f1Hf2b;
G,EE∂f′∂

18、f′∂f′11∂u1∂v′′′′=·+·=−2yf+2xf,..................591112∂y∂u∂y∂v∂y∂f′∂f′∂f′22∂u2∂v′′′′=·+·=−2yf+2xf,..................69∂y∂u∂y∂v∂y2122∂2z′′′′′′′′′=2x[−2yf+2xf]+2f+2y[−2yf+2xf]∂x∂y111222122′′′22′′′′=2f−4xyf+4(x−y)f+4xyf...........................792111222P∞4n2.y-

19、'm5.n=15n−3n4n4n+1e:un=5n−3n,un+1=5n+1−3n+1.....................................29u4n+15n−3nn+1lim=lim×.......................................49n→∞unn→∞5n+1−3n+14n31−()n5n−3n45=4lim=4lim=<1....................69n→∞5n+1−3n+1n→∞355−3()n5EDR0'Vy6gSm.....

20、........................................79(89)>

21、u_F++P(6,−3,2),H

22、u4x−y+2z=8U,

23、u7.−−→e:

24、uF++P(6,−3,2),2

25、uH1oOPH?S

26、u4x−y+2z=8'61on0={4,−1,2}.

27、4,2

28、u'61og'ijk−−→n=OP×n0=6−32=−4i−4j+6k......................494−12d5f2f#jA!9e_}9_℄CWE

29、u'7'−4x−4y+

30、6z=0,2x+2y−3z=0.....................8922((89)3Gf(x,y)=x+y−2lnx−18lny'V.′2fx(x,y)=2x−=0,xe:D&x=1,y=3...............................2918f′(x,y)=2