✔ 最佳答案
f = cos(3xy) = -1
fx = - 3y sin(3xy) = 0
fy = - 3x sin(3xy) = 0
fxx = - 9y^2 cos(3xy) = π
fyy = - 9x^2 cos(3xy) = 9
fxy = fyx = - 9xy cos(3xy) = 3π
f(x+h, y+k) = f(x, y) + 1/2 [fxx h^2 + 2 fxy hk + fyy k^2] + ...
f(1+h, π/3+k) = -1 + 1/2 [πh^2 + 6πhk + 3πk^2] + ...
Choose h = 0, k = - π/30, then f(1, π/3 - π/30) = cos(0.9π)
cos(0.9π) ~ -1 + 1/2 [3π(π/30)^2] = -1 + π^3 / 600 = - 0.948
Choose h = - 0.1, k = 0, then f(0.9, π/3) = cos(0.9π)
cos(0.9π) ~ -1 + 1/2 [0.01π] = -1 + 0.005π = - 0.984...
cos(0.9π) = - 0.951...
2010-07-25 00:54:21 補充：
Correction:
fxx = - 9y^2 cos(3xy) = π^2
f(1+h, π/3+k) = -1 + 1/2 [π^2 h^2 + 6πhk + 3πk^2] + ...
Choose h = - 0.1, k = 0, then f(0.9, π/3) = cos(0.9π)
cos(0.9π) ~ -1 + 1/2 [0.01π^2] = -1 + 0.005π^2 = - 0.95065...
cos(0.9π) = - 0.95105...
2010-07-25 16:37:00 補充：
其實好多組數字都可以係答案，冇話一定得一個，
如果單以上面兩組數字黎睇，後一組好似好D...
睇下邊個答案計完出黎個誤差比較細D就得。
