2004考研数学二试题及解析.pdf
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2004
. 6 4 24 . .
(n −1)x
1f (x ) lim 2 , f (x ) x ____ .
n→∞ nx +1
0
x 0 f (x ) 0
1
(1 )
− x
( 1) 1
n − x x
( ) lim lim n
x ≠0 f x 2 2
n→∞ nx +1 n→∞ 2 1 x x
x +
n
0, x 0
⎧
⎪
f (x) ⎨1 ,
⎪ , x ≠0
⎩x
1
lim f (x ) lim ∞≠ f (0)
x →0 x →0 x
x 0 f (x ) .
⎧ 3
x t +3t +1
⎪
2y (x ) ⎨ , y y (x )
y t 3 3t 1
⎪⎩ − +
x _______.
−∞1∞
dy
2 2
dy dt 3t −3 t −1 2
−
,
1
dx dx t 2 + t2 + t2 +
3 3 1 1
dt
2
′
d y d dy dt 2 1 4t
⎛ ⎞ ⎛ ⎞
,
2 ⎜ ⎟ ⎜1− 2 ⎟ ⋅ 2 2 3
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