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2009年温州大学数学分析考研真题618.pdfU s \0 _ 2009 8 ‘ + F C _ - I \0 M _ \0 V \0 (A) I R
1. (7× 6
′
= 42 \0 ) ’ O W 4 \0 Q (1) lim
n→∞
(
1
√
n
2
+1
+
1
√
n
2
+2
+ ... +
1
√
n
2
+n
);
(2) lim
x→a
sin
2
x?sin
2
a
x?a
; (3) lim
x→∞
(1?
2
x
)
?x
;
(4) e t Z > \0 \0 \0 > 5 & L \0 # " L \0 x+
x
3
3
+
x
5
5
+···+
x
2n+1
2n+1
+···;
(5) ’ O \0 \0 $ \0 Z
+∞
0
e
?ax
?e
?bx
x
dx, ; q b > a > 0;
(6) ’ O I =
I
L
xdy?ydx
x
2
+y
2
, ; q L T B b \0 \0 ! i \0 \0 \0 ? h \0 \0 * Y \0 (7) E F(x,y) =
Z
xy
x
y
(x?yz)f(z)dz, > F
xy
.
2. (8 \0 ) e " L % X \0 ε?δ \0
m 7 \0 (1) lim
x→1
x
2
?1
2x
2
?x?1
=
2
3
; (2) lim
(x,y)→(0,0)
x
2
y
x
2
+y
2
= 0.
3. (10 \0 ) ? K " L % X lim
x→+∞
f(x) \0 ) i k \0\0 e P m 7 lim
x→+∞
cosx \0 \0 j \0 4. (10 \0 ) E " L f(x) j \0 ? ( [a,b] D 2 ^ ( k f *), e A * i / m 7 f(x)
j [a,b] D \0 j u \0 o \0 5. (10 \0 ) E f(x) =
(
x
2
,x≥ 3,
ax+b,x < 3.
> a,b \0 o \0G f(x) j x = 3 ? .
\0 \0 6. (10 \0 ) E " L f(x) j [a,b] D . \0 \0m 7 \0\0 j ξ∈ (a,b), G \0 2ξ[f(b)?f(a)] = (b
2
?a
2
)f
′
(ξ).
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