文档内容
-,�:ll� ( *�:it 10 ,J,�, �,J,� 5 :St, :it 50 :St. =A:�1J,��lli a{] lm1'"�:Igicp, R �-:Igir4,g.� §
� * ,
m.PJr� m�
:IgifiJ a{] *-m::t,l=A:� Ja a{] P-J. i
(A)/(1 ) = 0. (B) limf(x) = 0.
x-1
(C )f' ( 1 ) = 1. ( D) lim f' ( x) = 1.
x-1
( 2) i!l.J( u) nJ � , z = xyf ( : ) , ;ff x ;; + y ;; = y 2 (ln y - ln x) J!U ( )
( A )J(I ) = ; , f' (I ) = 0. ( B )/(1) = 0, f' (1) = ; .
( C )/(1) = ; ' f' (I) = 1. (D )/(1) = 0, f' (1) = 1.
(3) i!J.�3'tllx n f tWJE - ; � Xn �; ,JJ!U( )
(A) ;fflim cos(sin xJ Htf,JJ!tllim x Hi£.
n
n-1>00 n-oo
( B) ;fflim sin( cos xJ Hi£, JJ!Ulim x Hi£.
n
n---+oo n---+oo
(C ) ;fflim cos( sin xJ HtE,JJ!Ulim sin x HtE,f!=llim x �-JEHtE.
n n
n......-+00 n-oc n----J>oo
-- -- --
( D) ;fflim sin( cos x ) Htf, JJ!Ulim cos x Hi£, f!=llim x �-JEHtf.
n n n
l' l' l'
x ln (1 + x ) 2x
(4 ) -;('; -+.>- / 1 = O 2( 1 + COS X ) dx ,/ 2 = O 1 + COS X dx ,/ 3 = O 1 + Slll . X dx,JJ! U(
(C)/ < l < l , (D)/ < I < I .
1 3 z 3 2 i
(5) r3itl 41'"�f4i:r ,3 �mli$ A nJfflfp,txtffl1t�-1--1t:5t��&,��f4¾( >
( A)A � 3 1--�jP] a{J�filffl.
U
(B)A � 31'-ttx*�tffilfPJ::I:.
( C)A � 31'-WilWil�'lix*a{JtffilfPJ::I:.
(D ) A � � r � F8'J tf filffi � �fil fPJ ::l:;i:§ 1Lil: 5':.
(6) i!l.A,B -jJ n �mli$,E -jJ n �1'ifilmli$,;ff1f�f].Ax = O -SJ Bx = O F8'.lflilf,JJ!U(
(A)(�
�)y ,R��--
= 0
A
,R��--
(B)(:
= 0
A B)y
- 1 -r r r 2 r
(7) ia_:a1 = (,\,l,l) ,a2 = (1,,\,l) ,a3 = (1,l,,\) ,a4 = (1,,\,,\ ) ,*a1,a2,a3 l§a 1 ,a 2,
a �111-,Intl,\ 1¥Ji&ffim:lll¾C )
4
(A)jo,11.
(B)j,\I ,\ ER,,\ �-21.
(C)j,\I ,\ ER,,\ �-1,,\ �-21.
I,\
(D)j,\ ER,,\ �-11.
( 8) ia:il.lf!t!IZ:lfll: X ijll,b\lKl'aJ ( 0 ,3) J:1¥J:f:5]�5t1!l, il.lf!fJL�:11: Y ijll,b(��j;J 2 1¥JrEJt't5t1!J ,Ji X 1§ Y
1¥]tf}jJ�jg - 1,Jiltl D(2X -Y + 1) = ( )
(A)l. (B)5. (C)9. (D)l2.
(9 )ia:il.lf!fJL�:11: x l ,X 2 , .. · ,X n J!.lt:fr.[P)5t;fp, liX 1 l¥J 4 Wi'�l=H'=ftE, E(X�) = µk ( k = 1 ,2 ,3 ,4), Jntl�ffl
I � � I�
tJJ tt�x��:rt . x -tffxt 8 > 0 ,iHf P{ X7 - µ 2 e } :s; ( )
( 10) ia:il.lf!flL�:11: X - N(O, 1), *tE X = x 1¥J�ftj:r, il.lf!flL�:11: Y - N(x, 1) ,JntlX 1§ Y 1¥Jffl:k*�
-'jg ( )
1 1
(A) 4 · (B) 2·
= .
*��
s �, �
.:tl��( 6 1J,� fif1J,� 30 � ,ffi��:I-A1£�i:J:IIU£...t. )
1
= 2 2
(11) rn�f(x,y) X + 2y tEi�(0,1) 5tti¥1:ll*nlPJ��-'j;J __
(12) f"' ln x dx = --
,Jx
I
(13) � X � O,y � 0 Bt,x 2 + y 2 :s; ke•+y •tgJi.lt:fr.,JilU k 1¥JJ!Rffim:llf¾_ _
I00
' =
(14) EJ�o�� n � e -nx 1¥] i&��j;J (a' + 00 ) 'mu a --
n
n=l
(15) B���A fl1 E -A PJ:ifil:,:Jt:q:i E j;Jif!f:IL��.*�� B mL@[E - (E -A)-1 ]B = A, Jntl
B -A= --
(16) ia: A,B ,C j;Jll.lf!f]Lfi:ftj:, Ji A 1§ B ][�ffl�,A 1§ C ][�ffl�,B 1§ C ffl][J!.it:fr.,P(A) =
P(B) = P( C) = ; ,JiltlP (B U CIA U B U C) = __
-2-= ..
M�lffi( *lm3t 6 ,1,�, 3t 70 � .-��� l±Dt*i�JJ.I, iiEPJ.13:1�:§;!tMi-�ill. )
m
< 11 ) < * :JI * 10 * )
i&Ul§�y(x) �vt{(jtjf;fiy' + \_y = 2 + ✓x89n!J.JJE�14r(l) = 3 B9fff,*
2 vx
lilt� y = y(x) !'fJitJri!r�.
<*:!mijt
(18) 12 jj-)
- 2
E,9;11-"Sjl-ffi[R� D = 1 (x,y) I y - 2 � X � )4:y2,o � y � 2 i 'it� I= ff(� Y� dxdy.
+ y
D X
< < *:!m* *)
19) 12
B9;1llilt�L�liltffi.!:4x 2 +y 2 +i = 1,x�O,y�O,z�OB9:itl!/.,liltffi.!JfrPJ:im_t,lilt�L
f
B9Jf lPJ;j;!lliltffi.! B9 Jf 1Plrq:-if ,t"-¥f!JJ!tl, it�/ = (yi � cos z) dx + 2xidy + (2xyz + xsin z) dz.
-3-*REm53"
( 20) ( 12 53")
ti¾:Rl§fiJ(x) :fl:( - 00, + 00) _t�=!m-:li��fi, iJEijij: J"(x) ;;.,, 0 fl9JE#!IZ,�
�-flj:¾xif1f1t�fiiJEl9�fic a,b,�� !( a ; b) :;;; � ff(x)dx J/x.fl.
b a
3 3
L L
ti!:=7X.�f(x 1 ,x2 ,x 3) = ijx,x j .
i;J j;I
(I) �l±lf(x ,x ,x xifmIE19�1I$;
1 2 3)
( II)3JtiE3t�� X = Qy � J( x 1 ,x2 ,x 3) 1t1-Jfffi7ftf�;
( fil) >ltf(x l ,X z ,X 3 ) = Q fl9 •.
<*REm53"
(22) 12 53")
t¾: X1 ,X2 ' ... ,Xn 1-1* § :f:5],(ajg 0 El9ffifil5J";{p -�,�E19ffiiliMitJLf-F*' Y I ' Y2 ' ... 'y m 1-1* § :f:5],(a
1-128 E19ffific5J";/p,�,�E19ffiiliMitlLf.F*,ilWJf.F*;i:tl!f.�fl.Jtrp 8( 8 > O) ¾*��fic. llJJfl
·*
f-F* X1 ,X2 ' ... ,X
n
,Y1 'Y2 ' ... ,Ym 8 El9:i'i7d�f'&filrtt:I: 0,#>Jt D(O).
-4-