推 zxc321:謝謝 太感謝了~~ 59.127.194.112 03/28 18:49
※ 引述《zxc321 (堅持到底 )》之銘言：
: 1.Let f(x) = (1+x)^ (1/2) + (1-x)^ (1/2)
: (a) Find the Maclaurin series for f
: (b) Find (4) (51)
: f (0) and f (0)
: 請問(a)是要我導馬克的公式嗎? (b)小題 我不會算
: 2.
: (a) Evaluate ∫∫ e^(x+y) where R is given by the inequality
: R
: ｜x｜+｜y｜≦1.
: (b) Let f be continuous on [0,1] and R be the triangular region with
: vertices (0,0),(1,0)and (0,1) show that
: ∫∫f(x+y)dA = ∫[0,1] uf(u)du
: R
: 謝謝~~
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1.
∞ ∞
(a) f(x) = Σ (0.5 C k)(x^k) + Σ (0.5 C k)((-1)^k)(x^k)
k=0 k=0
∞
= 2 Σ (0.5 C 2k)(x^(2k))
k=0
(b) (4)
f (0) = 2(0.5 C 4)(4!)
(51)
f (0) = 0
2.
(a)
令 u=x+y,v=x-y
1 1
所求 = ∫ ∫ exp(u) du dv
-1 -1
= 2(e-1/e)
(b)
令 u=x+y,v=x-y
1 u
所求 = ∫ ∫ f(u) dv du
0 -u
1
= ∫ 2u f(u) du
0
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