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K8 1. ‰eÍë?Í +∞ an ¬Ò5ø`2nd:
n=1 (1)a = 1 ln1+√1 ;
n1 n+1 n3
1 n+1 n2 (2)an=3n· n .
K8 2. ‰oÍë?Í
K8
Oé
Ÿ• K8
K8 øÖ
5. â1⁄2Ç°
T ={(x1,x2,x3)∈R3| x1 =(2+cosθ1)cosθ2,×2 =(2+cosθ1)sinθ2,×3 =sinθ1,
dσ ¥ T ̨°».
6. œLÈÎÍ α ¶Oé
I(α)=
ˆπ 2
0
|x3 |dσ, T
ln(sin2x+α2cos2x)dx, α>0.
0≤θ1,θ2 ≤2π}. ˆ
+∞
(−1)n
x+n 3 E = [0, +∞) ̨òó¬Ò5ø`2nd.
K8 3. ÚeoÍ–mèç1⁄2?Í:
(1)Ú 1(chx+cosx)3x=0?–mèTaylor?Í;
2
(2) Ú f (x) = chx, −π ≤ x ≤ π –mè Fourier ?Í.
K84. â1⁄2oÍf(x,y)=(2×2 +y2)e1−x2−y2.
(1) ¶ f (x, y) 3 R2 ̨§k.:, ø‰= ¥4ä:; (2)¶f(x,y)3 ±S:={(x,y)∈R2|x2+y2=1} ̨Ååä⁄Åä.
n=1
7. oÍ f(x) ∈ C([0,a];R) øÖ f(0) ̸= 0, oÍ S(x) ∈ C1([0,a];R), 0 < S(x) ≤ S(0) S′(0) ̸= 0. y2:
ˆa f(0)
f(x)Sλ(x)dx ≃ −λS′(0)Sλ+1(0), λ → +∞. 0
1