01.Esercizi1
description
Transcript of 01.Esercizi1
a) Determinare, se esistono massimo, minimo, estremo superiore ed es-tremo inferiore dei seguenti insiemi
1) A =
{n− 1
n+ 1, n ∈ N
}
2) B =
{n− 1
n+ 1, n ∈ Z, n 6= −1
}3) C =
{x ∈ IR : x3 ≥ 1
}4) D =
{x ∈ IR : x2 + 1 ≤ 5
}5) E =]0, 1[∩Q
6) F =
{x ∈ IR : x > 0,
1
x≤ 3
}
7) G =
{x2
x2 + 1, x ∈ IR
}
8) H =
{(−1)n 1
n+ 1, n ∈ N
}
9) I =
{x
x+ 1, x ∈ IR, x 6= −1
}∩ {−2 ≤ x < −1}
b) Dati i due insiemi
A =
{x ∈ IR :
x+ 3
4− x2< 0
}B =
{x ∈ IR :
x(x− 1)
x+ 2≥ 0
}
determinare A ∩B e A ∪B.
SOLUZIONI
Esercizio a)
1) minA = −1, supA = 1
2) minB = −1, maxB = 3
3) minC = 1, supC = +∞
4) minD = −2, maxD = 2
5) infE = 0, supE = 1
6) minF = 1/3, supF = +∞
7) minG = 0, supG = 1
8) minH = −1/2, maxH = 1
9) infI = 2, supI = +∞
Esercizio b)
A =]− 3,−2[∪]2,+∞[, B =]− 2, 0] ∪ [1,+∞[
A ∩B =]2,+∞[, A ∪B =]− 3,−2[∪]− 2, 0] ∪ [1,+∞[