首都师范大学数学专业历年考研真题

HNfi%x>OR
lim f ( x + n ) = O (n%iEP%) . 3%:lim f ( x ) = O . X-++m
I
"
:
729
3
3
3
%
# 3 x
b o o 0
S = (al,a2,a3,p)
%as-'AS =
[:
O O O a ],S+a7b3~1)+dt1#b9&~
t
( 0
1. % A
E
2.
~ ~ i t ~ f a,COS ~ i t s j ~ ~,I ~ +~' w * 4~ + E~ x ~ E W Z. $ ~ 5 ~ . ~ , ~ ~% [ 0
X
UT-%~E~Z~JB~A;~.~~SB -, ( $ 3 8 9 ) E # E E - S B X ~ ~ E ~ B :
%%~%i&%jW$%&BfiRI, %%~&@Z$ke
+,
(zfrW12e)
%.
zx
8f ( x ) S ( - ,
+co)_tFJq, H % B B ~ ' ( ~ ) ~ E ( - - ~ o ,4-BE +~)
x~(-m,+oo),
f,(x)=n{f(x+n-')-f(x)},
1.
n=l,2,-.-.
1 (16*) g V % @ $ & F k & # n . b?3~@&b'!J%'E~1'~, A, B, g ( X ) = AXB + CX + XD. za: C , D E V. X$fE& X E V ,
1. u
gvm
~ ~ ~ ~ & ;
a
2.
3 C = D = 0 El*,
%qs%&kg@HE?kj lABl#
+ ax2 + bx x2" + 1
m.
n--to3
( 1 0 f f ) iEa: lim an = 0.
3 an > O, i
n = I , 2, - ..,
n-+w
lim
an+l
=1
> 1, ~d
I'
.
(12 f f ) 3 @ % f ( x ) & [ O 1 + ~ ) 1 % E f 1 l ( < ) , H f ( 0 )= O . xO iiEsB: X.f'43XN > 0, Y > 0, G ~ ( x + Y< f ( x ) + f ( y ) . x ) ( 1 2 *)
(16
?L. (16 5$) 8V g%%i& k& n gE%'t@[a, R +IZ%ZB. iZ4'~[ a , p ] , $,~WT~EE:
1) [ka, B] = k[a, B], X;f-ffr& a, E V,I; E 8; p
V
ksx-
2) [ a + D, rl = [a,7 1
+ [B, Y] Xt{iE%?a, 7 E V; PI
3) [a, 8 = -[B, a],XfliE& a , P E V ; 1 4)
X;f'{Z% a E V \ {O), $FY$ fl E V, I$.!$# [a,p] # 0, V % S- ?2[6J.& n !$t S- 9[4V m!+$TPJlb7%:
-k,
(%l/J\f@8+, %2~h@7#, %15!&)
M n ( R )$3-+iEBH$$$EP$. iiEaAGZEiEX~~~3EPf A = B 2 . B 12?+ 2. B A E M,,(lR) S-+n PfiFJ'S%EE. iiEn8@7ZiESH%%EP$ UBE?ZS*lrfU ' f @$+A= U . P
WEW;
3. % f ( x ) Brl%E%%@, ( x ) &El@ (Z%;FZktiR%%%&i-;%892A) %F f .
A.
(*a15 j f )
1.
+oO
iQ f ( x ) B [a, + m ) l @ 1 P R , H%BE%!+
if
(x)rh&&.
a
Z%:f ( x ) 2 O , x ~ [ a , + m ) ;
33-1
= (
a b c d )lu,btC,a+d=O
. & ~ - A E V , Z X Yi f h % L a L T
TI,
1,
1
%1/1\%83, %2/j\%73-f,
&15%)
i f (s)?l[n.b]Ljit$, iltw f ( s ) $ [ u , b ] l & ~ T T R ~ % i % i . 2
lim
x+l
-2x2 +llx-6 x 2 -2x
= -3.
-, -
(ZbT.3125')
3 i 3 % f B ( a y b ) _ t : S 4 g , f(a+O)=-oo,
E = (x E (a, b ) f ( x ) 2
1.
I
01,
f(b-O)=+co. i zx, = inf E.Bl%%?z%lx
E%fiSf;-
3. iEq:
+ ( A ) %TiJZERBtl%5+&~3?&1+E B A%
tFJt+E@.
I\.
5$)i!? A A n b?%z%, ,B #l%$G%&&k ?t$l]lfil@. X n iiEs!: %8i%ZT24EAX = P Gf&$@Jtlfr;%&\~&1kE@ % P -VT A'X = 0 /!I!Jj@fg@ . Wj 9 E
+L. ($3103) it%%%
I ="
1a + dx 2x , , cos
g+%&a>l.
j 3 (12 !&) - .
&Ern%L&E%%.i z OE = { ( X I Y I) &
f ( x ,y ) G@-@m%+ y2 F 1 k % & i & x2 %%f%,
-x <
2 + y 2 1 I),%*
-. -
(12 f f )
3@%
x2n-1
f ( x ) = n-im lim
%' If(x)I 5 Mo, IfU(x)I5 M2, fFq Mo, &A9 x E (O,+m), Ifl(x)l < 2 ; k
(12
a@&c x ) a (0,+OO) +-IMJB, r axtlma
E ( 0 ,+w),
Jm.
M2
%iE%%.
iE : X f 3 i a .l
9) f i.$
iZ%: & a x n E E , n=1,2;..,I3$%xn +x, ( n - c o ) ;
Z,
(&ElO5?)
@ i % & p i % ( a , b ) k - B S % , @ % f & [ c , d ] L i S % , l3H-9~ x E (a, b), & p ( x ) E [c,d l . iiE#: B++i%& p $ ( a ,b ) k - - & S i % . f o
f ( O ) f ( l )> 01
f"(4> 0
( x
1
1
/ f(x)dx
1
0
= 0-
iiEsa: ( 1 )
f (x) ( 0 , l ) l%R%rn?%,6; ( 2 ) G&--,5 t E ((),I), @ f'(C) = S,I f ( t )dt.
a
h- (10 *)%%%k C a n 3 C c n %$@€&,& 6 3 J 2% 3
iZ%%& C bn &&@.
(12Jf) B I ( x ) = J 0
+OO
+.
+-.
mdt,XiE:
e-'z
i ( 1 ) I ( x ) 7% (0,+co) k%%,J3 lm I ( x ) = 0; z++m
( 2 ) I ( x ) 7% (0,+m)
(12
mFri%.
!&) iiErn@%
2.
XEN-m
x E [a,b] , % f( x ) # 0 , iiEaB: AE%& M , Jt M , , I2@% n ftftkef, N-tn x E [a,b] , f M , 5 lnlfn(x)( < M 2 .
I
lb7: f(x, ) ?ZA (0,O) @%BX#? iiE%$%@~%ie. y
*+a+
x+b-
X-+a+
x+b-
I
i$-+$$$#$i& f i Q % & 8 E X I , %%{&@%$ko %
5.
(*W20*)
iQ f ( x ) =
(x -3)' , BPffR( x ) mwFB&: f 4 ( - 1) ~
1. % f ( ~memrs71.nBm; )
.
2. % f(x)BtlAl
2.
Fg [El.
$2 n > 2 , U 2 V B.tl-+& iiEN UL # {O}.
3.
a $ U P !ik&fiST2l'a7.U_ # 0. [a,@]
4. B5@;f-E--tfE7f:~Zt.Ilib Ji&flB&. S- 9 l ?
.
(12 53) E f ( x ) $E [O, 1 k83?%&, 1 H
+,
1.
iiE@la:X f { 3 8 a , P , r E V , k . ~ R,%[cr,kp] =k[cr,B], [ y , a + B ] =
I Y , ~ I + [ Y , ~ I ,[ a , a ] = O .
2 a $3 V k b ~ - - + R J 3 ~ f k ~ @ - € l . ~ E : E V , X 4s cr,B f 3 % [ a ( a ) , a ( B ) ] = [a,@]. 8 U E V H--+ a- ;; ? ? IK . I3 ? 9' $ J u'- = (11 E V I [ u , ~= o , x + { ~ & u U}.iIEY UL $& V 69 a- $9 ] E
0.
h.(18 %) % C 3 D % n PfigEg,
iiEg:
1.
2.
A
= C'C,
B = DID, A, p
g&$K P, XA -k pB = P'P; C 3 D z-%qi!!!E%, Jgk%E% q%. P
-k.
(16 *) A 8
3 B $&Eq ng#kE%, n $(A)
(x)
a [o,+m) L%%, E f ( x ) > 0. gq L
1.
%I$ @T:
lim
tan x - sin x , *+o sin3x
7 , (*%lo&)
RE-~ZX~~ESB: lim
x+1
x2 - 1 =-2. 3x2 - 7x + 4
1.
ZH: lim f ( x ) N F R f(x)@G&, Hlim f ( x ) . l i m f ( x ) > O ;
ZYI :
If,( X I ) B (-,
+a)
l-awr Y(X):
6
n-w
2.
tr%: R f f f t a , b ~ ( - c o , + m ) ,t l i r n l f n ( x ) & = f ( b ) a
f(n).
-I--\ (%1* &!5)
n-w
SB&f(x)$E[Oy+~)+-B2E$%,