Esercizi svolti di analisi reale e complessa - Dipartimento di ...

• M1 = ( 2
√ 3 , 1
√ 3 ) M2 = (− 2
√ 3 , 1
√ 3 )
f(M1,2) = 2
3 √ 3
• m1 = ( 2
√ 3 , − 1
√ 3 ) m2 = (− 2
√ 3 , − 1
√ 3 )
f(m1,2) = − 2
3 √ 3
maxD f = 2
3 √ 3 minD f = − 2
3 √ 3
∂ ∂xi g(|x|) = g′ (|x|) ∂|x|
∂xi = g′ (|x|) xi
|x| . ∇g(|x|) = g′ (|x|) x
|x|
P1000(s, t; 1, 0) =
1000
α∈N 2 |α|=1
P1000(x, y; 1, 0) =
aβ =
(−1) α1+α2+1 (α1 + α2 − 1)!
(s − 1)
α1!α2!
α1 t α2
1000
β∈N 2 |β|=1
(−1) β1+1 (β1+ β 2
2 −1)!
β1!( β 2
2 )!
aβ(x − 1) β1 y β2
β2
0 β2
f ∈ C ∞ (R 2 \ {x = 1})
{(1, y), y = 0}
∂
x = 1
n f
∂xh ∂yk y
−( e x−1 )2 P (y,x−1)
Q(x−1)
limx→1 Q(x − 1) = 0
x → 1
Py ≡ (1, y)
f y > 0
y < 0
y = 0
(1, 0)
C1