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

∀ k ≥ 0 f ∈ C k ({0})
f ∈
C 2 (0)
P6(x; 0) = x1 + x1x2x3x4 + o(|x| 6 )
P3(x; 0) = x3 + x1x3 + x2x3 + x2
1 x3
o(|x| 6 )
δ = 1
4e
2
x22
+ x3
2
+ x1x2x3 +
f ∈ C(Rn sin |x|
\ {0}) lim |x|→ 0 |x| = 1
f ∈ C(Rn )
f ∈ C1 (Rn \ {0})
f ∈ C1 (Rn )
R ∗ ≡ {(x, x) | x ∈ R \ {0} }
f ∈ C ∞ (R 2 \ R ∗ ) f
R ∗
3
P1 = ( 2
3 (− 2
sup f = +∞ inf f = −∞
1 , √ ) P2 =
6
1 , − √ )
6
D
Py = (0, y) (−1 ≤ y ≤ 1)
• Py 0 < y ≤ 1
• Py 1 ≤ y < 0
• P0
∂D ≡ {x 2 + y 2 = 1}