Re: [代數] 求解三道題目！
7.
P(2,4,1)
n = (1,-2,1)/sqrt(6)
F = (x^2 - y^2)/(z^2)
grad F = (2x/(z^2), -2y/(z^2), -2(x^2 - y^2)/(z^3))
grad F| = (4, -8, 24)
P
答案 = grad F| * n = 44/sqrt(6)
P
9.
x = e^(-2t), y = e^t
dr = (-2e^(-2t), e^t)dt
F * dr = [(y^3)(-2e^(-2t)) - (x^2)ye^t ]dt
= [-2e^t -e^(-2t)] dt
S F * dr = -2(2 - 1) + (1/2)((1/4) - 1)
= -2 - (3/8) = -19/8
10.
L = 2
a_n = 0
L
b_n = (1/L)S x * sin(nPi x/L)dx
-L
= -[2/(nPi)](L^2)(-1)^n
= [8/(nPi)](-1)^(n+1)
Series = Sigma {[8/(nPi)](-1)^(n+1)} * sin(nPi x/2)
n = 1,2,3...
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