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K8 1. ‰eÍë?Í +∞ an ¬Ò5ø`2nd:
(1) an = (2n−1)!! ; (2n)!!
(2) an = nn·en . n!
K8 2. ‰oÍë?Í
3e ́m ̨òó¬Ò5ø`2nd: (1) E1 =[0,1−δ0],Ÿ•0<δ0 <1; (2) E2 = [0, 1].
n=1
+∞
(−1)n
n xn n=1
K8 3. ÚeoÍ–mèç1⁄2?Í: (1)ÚSi(x)= ́x sintdt3x=0?–mèTaylor?Í;
0t
(2) Ú f (x) = shx, −π ≤ x ≤ π –mè Fourier ?Í.
K84. â1⁄2oÍf(x,y)=xyln(x2 +y2).
(1) ¶ f (x, y) 3 R2 ̨§k.:, ø‰= ¥4ä:; (2)¶f(x,y)3 ±S:={(x,y)∈R2|x2+y2=2} ̨Ååä⁄Åä.
K8 5. 3•° Σ := {(x1, x2, x3) ∈ R3| (x1)2 + (x2)2 + (x3)2 = 1} ̨O黩 ˆ
df1(x) ∧ df2(x), Σ
Ÿ• f1(x) = sin(x1), f2(x) = 1 (x2)2. 2
K8 6. Oé¢%ÇN
T ={(x1,x2,x3)∈R3| x1 =(2+ρcosθ1)cosθ2,x2 =(2+ρcosθ1)sinθ2,x3 =ρsinθ1,
N».
K8 7. y2: x → +∞ û,
ˆ +∞ x
+∞ Γ(α) tα−1e−tdt ≃ e−x
k=1 Γ(α−k+1)
xα−k.
0≤ρ≤1,0≤θ1,θ2 ≤2π}
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