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

Q = {0} × R y
x = 0 Q0 = R
l =
limn xn
ɛ > 0
{Rn} N n=1 N n=1(Rn) < ɛ
∀ ɛ > 0, ∃ N > 0 xn ∈ [l − ɛ, l + ɛ] n ≥ N
Rk = {xk} k < N
RN = [l − ɛ, l + ɛ]
{xn = n}n [0, 1]
9 i) 4
π ii) 24
e 1 iii) 4 − 2
1 iv) 12
D ≡ {0 ≤ y ≤ 1, y2 ≤ x ≤ 1} = {0 ≤ x ≤ 1, 0 ≤ y ≤ √ x}
D ≡ {0 ≤ x ≤ 1, 1 − x ≤ y ≤ √ 1 − x2 }
1 1
1
x − y
dy
dx = −
(x + y) 3
0
0
0
1
dy
0
y − x
dx =
(x + y) 3
1
0
dx ′
1
0
x ′ − y ′
(x ′ + y ′ dy′
) 3
x ′ = y
y ′ = x