2004.数学三.pdf
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2004
sin x
(1) lim (cosx −b) 5 a =_________b =___.
x
x →0 e −a
1, −4
sin x
lim (cos x −b) 5 lim sin x ⋅(cosx −b) 0
x
x →0 e −a x →0
lim (ex −a) 0 a = 1.
x →0
sin x x
lim (cosx −b) lim (cosx −b) 1−b 5
x →0 ex −a x →0 x
b = −4.a = 1b = −4.
(2) f (u , v)f [xg(y ) , y ] = x + g(y )g(y )g(y ) ≠ 0
2
∂ f
.
∂u∂v
′
g (v )
−
2 ( )
g v
u
u = xg(y )v = y f (u , v) = +g (v)
( )
g v
2 ′
∂f 1 ∂ f g (v)
− .
∂u g (v) ∂u∂v g 2 (v)
⎧ x 2 1 1
,
xe x
− ≤
⎪ 2 2 2
3 f (x) ⎨ 1 ∫1 f (x −1)dx .
⎪ x 2
−1 , ≥
⎩ 2
1
−
2
2 1 1
x − 1 = t∫1 f (x −1)dx ∫−1 f (t)dt ∫−1 f (x)dt
2 2 2
1
2 1 1 1
2 x
xe dx + − dx + − − .
∫−1 ∫1 ( 1) 0 ( 2) 2
2 2
4 f (x , x ,x ) (x +x )2 +(x −x )2 +(x +x )2 .
1 2 3 1 2 2 3 3 1
2
1f (x ,
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