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

f(x, y) = x 2 y + 3y − 2 (x − 1)
(y + 2)
f(x, y) =
y
x
e −t2
dt
K ≡ {(x, y) ∈ R 2 : 0 ≤ x ≤ y ≤ 2x}
f(x, y) = (x + y)
D ≡ {(x, y) ∈ R2 x : 2
4 + y2 ≤ 4}
f(x, y, z) = xye −z2
D ≡ {(x, y, z) ∈ R 3 : 4x 2 + y 2 − z 2 ≥ 1}
T : C([−1, 1]) −→ C([−1, 1])
T u(x) ≡ x
2 u(x ) + g(x) .
2
g T
T T
∃! u u = T u
T : C([−a, a]) −→ C([−a, a]) a > 0
f : R 2 −→ R
(x, y) −→ f(x, y) = −xe y + 2y − 1 .
P0 = (x0, y0) x0 ≤ 0 f(x0, y0) = 0
P0 y