中科院2006年数学分析试题.pdf

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ax + b Q x 0;
y = ≥
 2
x + 1 Q x < 0.
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∞ 1 ∞ 1
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2 (15 D ) an > 0,
Z
VHWH[
n=1 an VHWHX n=1 an+1
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1 m n
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3 (15 D ) m, n 0 x (1 x) dx
[
X 0
≥ R −
\ b cH`HdHeH`HfHJHK
4 (15 D ) a > 0, f(x) [ a, a]
− Xhg
a f(x) a
dx f x dx.
x = ( )
Z−a 1 + e Z0
0 0
L
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5 (15 D ) f(x) [a, b] f (a) = f (b) = 0,
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ξ(a, b) FHy
∈ 4
f 00(ξ) f(b) f(a) .
| | ≥(b a)2 | −|
−
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6 (15 D ) f(x) [a, b] f(a) = 0,
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g
b
max f(x) √b a( f 0(t) 2dt)1/2,
x∈[a,b] | | ≤− Za | |
b 1 b
f 2(x)dx (b a)2 f 0(x) 2dx.
Za ≤ 2 − Za | |
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7 (15 D ) n D