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1996年考研数学一真题.pdf

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1、1996 M S V 3 dB I k B k5W# Ba A b5 1 !2lim 8,xxxaxa+=5 a = . s ln 2. W y33323lim lim 1 ,axxaxaxaaxxxa aexa xa + =+ = 38ln2aea= 2 !B V#()6, 3, 2 , O 428x yz +=“ O1nna=l 0, ,25) ()211tannnnnan=A l . BHq l . (C)? . D 1 . s A . W ()221tan tan ,nnnnanann=7 lim tan ,nnn = n sv H ()22tan 1nnna an . W y ()

2、() ()22sin , 2 cos2radsrrdad = = + = pL 0022cos 8sin 822|sada a =2 !()1110, 6 1, 2, ,nnxx xn+=+=“ k nx Kii pNK . W 12 110, 6 4xx x=+=21.x x ! k1kkx x+ 5 11266 .kkkkx xxx+=+ = #B ,EB M ,n 1,nnx x+ nx h . A ()01,2,nxn=“ nx / AK nx Ki . : lim ,nnx a= 16nnx x+= + H |K 6,aa= + V7260aa= 3a = 2a = y 0nx #

3、pK 3a = . a 19 w s()2,sx z dydz zdxdy+ S _ w ()2201zx y z= +E_ z_C . W 1 T1S V UE_ _ z_ ()2211,zxy=+D1S xOy g u5 () () ()()()112212002222 13sSSSDrx z dydz zdxdy x z dydz zdxdy x z dydz zdxdydV dxdyd rdr dz+=+= + = w32.2= +=W 2 O gEy 2, 2xyzxzy= () ()( )()()222222224 24 2xsSSDx z dydz zdxdy x z z z d

4、xdyx xz z dxdyx xx y x y dxdyd+=+=+= += 2122 3 2004 cos 2 cos.2rrr+=W 3 gE w S yOz gyzD w B 2,0 1,xzyz= Z_ -yNs |B 2,0 1,xzy z= Z_yNs |:xyD V U S xOy g u5 ()( ) ( )()()22222224yz yz xyyz xysDD DDDx z dydz zdxdyz y z dydz z y z dydz x y dxdyz y dydz x y dxdy+= += + + 211 2 1221004.2ydy z y dz d r rdr

5、= + = 2 !M2ux yvxay=+VZ22260zzzxxyy+ =e20,zuv=p .a W ,2 ,zzzz z zax uvy u v =+ = + ()22 2 222 222 222222 2 2222 22,22 ,44 .zz zzxu uvvzz zzaax yu uvvzz z zaayu uvv =+ + = + + = + | T Z ()()222210 5 6 0zzaaauv v+= G5i a 260,aa+ = O 10 5 0,a+ 3.a = a p) ()22112nnn= . W 7 ()221,1nnSx xn=5 ()22221122211

6、112 1 11212 111.22nnnnnnnnnnnnnnxxxSxxx xnxnxx xxxnx n=+= +=+= y()1ln 1 ,nnxxn= () () ()()11 1ln 1 ln 1 1, 0 ,2242xSx x x x x xx= + + + wL ()yfx= ( )( ),x fx) ML Y ()01,xf tdtxp()f x BVr T . W wL( )yfx= ( )(),x fx) MLZ () ()( )Yfx fxXx= 7 0X = () ()Yfxxfx= 5i () () ()01,xf tdt f x xf xx= () () ()0xf

7、 tdt x f x xf x = T x pe () ( ) 0xf x f x+ = ()()0xf x = s ()1,xfx C= yN () ( )1212ln .fx C xC C C=+ a i a ! ()f x 0,1 = O Hq ( ) ( ),f xafxb aba d c ()0,1 = iB ()2.2bfc a + W ()f x x c= ) TZ 7 () () ()( )()() ()2*2!ffx fc fcxc xc=+ + (), 0 1.cxc =+ ()*T 7 0,x = 5 () () ()( )()()210 0 0 , 0 c1, 2!ff

8、fcfcc c=+ + ()*T 7 1x = 5 () () ()( )()()221 1 1 , 0 1, 2!fffcfcc c=+ + TMh () () () ()( ) ()2 22111 0 1 2!ff fc f cfc=+ () () () ()( ) ()() () ()() ()()22212 2212211 0 1 2111 0 1222 1 .2fc f f f c f cff f cfcbacc= + + +y ()0,1c H()2211,cc+ # ()2.2bfc a + a !TAE= E n nd _ T 12AA= 1Hq 1;T= 2 1T= H A

9、V I . W 1()( ) ( )()222 2,TT TTT TTAE E E E = = + = yN( ) ( )2210TT T T TAAE E = = = y 0, 0T #2AA= 1Hq 1;T= 2ZEB 1T= H ,TAE= 0,TA= = y 0, # 0Ax = d ,yN 0A = A V I . ZE= 1T= ()20,AAAEA= = EA B ( 0Ax = y 0,TEA= 0Ax = d ,#( )A nyN A V I . ZE QE .L ! A V I 1,T = 2AA= 12 1,AA AA= AE= . TAE E= # A V I . a

10、 X=Q ()222123 1 2 3 12 13 23, 5 5 2 6 6f xxx x x cx xx xx xx=+ + 2. (1) p c#N=Q + (2) Z ()123, 1fxxx= V U =Q w . W 1N=Q 51315 3.33c= A y()2,=A # 0,=A N3,c = N H A 2. ()()51 3153 49,33 3=E - A p+ 1230, 4, 9. = 2 + V()123, 1fxxx= V U o . EaA b5 1 ! A B qsY 1 2 CV A B sY 60 40 B |Bq?C Q 5Q A q . s 3.7W

11、 ! Yq A = | A 3 B“ | B 3 C“ | Q ,5 () () ( ) ( )0.6, 0.4, | 0.01, | 0.02,PA PB PCA PCB= = = I q T ()()()() ( )()( ) ()( )|PAC PA PCAPACPC PAPCA PBPCB=+0.6 0.010.6 0.01 0.4 0.023.7=+=(2) ! , M O (V s220,2N M 5 M ()E = . s 2.W y , M O (V s 10, ,2N# Z =9V s O () ()110, 1,22EZ E E DZ D D = = =+=+= ()0,1

12、.ZN ()222220122222.xxEEZzedzzed+ + = = =EBa ! , M OVBs M X s p1,1,2,3,3Pi i = = ! ( ) ( )max , , min , .XY = 1 = M (),X Y s p Y X1 2 3 1 2 3 (2) p M X ().EX W 1 ( ) ( )max , , min , .XY =l 0PX Y= ( ) ( )1, 2 1, 3 2, 3 0,PX Y PX Y PX Y= = = OX 11, 1 1, 1 1 1 ,912, 2 2, 2 2 2 ,913, 3 3, 3 3 3 ,911 22, 1 1, 2 2, 1 ,99911 23, 2 2, 3 3, 2 ,999723, 1 1 ;99PX Y P P PPX Y P P PPX Y P P PPX Y P PPX Y P PPX Y = = = = = = = = = = = = = =+=+= =+ =+=# ps p Y X1 2 3 1 1929292 0 19293 0 0 192 X Hs X 1 2 3 P 193959# X ()13 5 2123.99 9 9EX=+=

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