华南理工大学期末考试《数学分析》数学分析-三-试卷快乐.pdf
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BACBD
M0 M0
E M0 M0 E
′ ′ 3 ′′ 2 ′′ ′′
2yf1 + cos xf2 + 2xy f11 + (sin x + 2x cos x)y f12 + y sin x cos xf22
′ ′ ′ ′
3 (f + f )dx + (f − f )dy
1 2 1 2
x+y 1 2 2 1 n 1 n−1
4 e = 1 + (x + y) + (x + 2xy + y ) + + (x + C x y +
2! n! n
+ yn ) + Rn eθ (x+y) n+1 1 n n+1
Rn = (n+1)! (x + Cn+1x y + + y )(0 θ 1)
5 2x + 4y − z = 5
∂u ∂u ∂v ∂v ∂w ∂w ∂w
= = = 1, , = y , = x, = −1,
∂x ∂y ∂x ∂y=−1 ∂x ∂y ∂z
w = xy − z
∂w ∂z
= y −
∂x ∂x
∂w ∂u ∂w ∂v ∂z
+ = y −
∂u ∂x ∂v ∂x ∂x
∂z ∂w ∂w
= y − −
∂x ∂u ∂v
∂z ∂w ∂w
= x − +
∂y ∂u ∂v
R = ∂z + ∂z = x + y − 2∂w = u − 2∂w ,
∂x ∂y ∂u ∂u
2 2 2
∂ z ∂ z ∂ z ∂ ∂z ∂z ∂ ∂z ∂z
2 + 2 + 2 = ( + ) + ( + )
∂x ∂x∂y ∂y ∂x ∂x ∂y ∂y ∂x ∂y
2
∂R ∂R ∂R ∂u ∂u ∂R ∂v ∂v ∂R ∂ w
=
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