Calculo I L01 Gab

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Ca´lculo I - Lista no¯ 1 - Gabarito - 1o¯ semestre/2016
1. Conjuntos:
(a) (b) (c)
1 4 3 1
2
(d) (e) (f)
−5 7 1
∅
0
(g) (h)
1 7 6043
2. Estudo do sinal:
0
5
+ −
(a) (b)
0
− 4
3
− +
(c)
0
−2 1
2
− +
@
−
0
− 1
2
+ −
(d) (e)
0
− 1
2
− +
(f)
0
−2 2
−+
0
+
− 1
4
3
0@
+ −
−3
@
−
(g) Sempre negativo. (h)
+
− 2
3
0
+
3. Fatorac¸a˜o:
(a) (x− 2)(x− 1) (b) (x+ 1)(−3x+ 1)
(c) −x(2x− 5) (d)
[
x− (1+
√
5)
2
] [
x− (1−
√
5)
2
]
(e) (2x− 1)2 (f) Polinoˆmio irredut´ıvel em R.
(g) (3x− 2)(2x+ 1) (h) (x− 1)(x2 + x+ 1)
(i) (x+ 2)(x+ 1)(x− 1) (j) (x−
√
3)(x+
√
3)(x2 + 2)
(k) x(x+ 3)(x− 1) (l) (x+ 2)(x+ 3)(x− 2)
Instituto de Matema´tica Universidade Federal de Mato Grosso do Sul
4. Resoluc¸a˜o:
(a) S=] −∞,−1[ (b) S=[3,∞[
(c) S=] − 2, 3[ (d) S=] −∞,−3[ ∪ ] 1
2
,∞[
(e) S=
]
0, 5
2
[
(f) S=] −∞,−4[ ∪ ]− 5
2
,∞[
(g) S=] −∞,−5[ ∪ ] − 5,−2[ (h) S= ∅
(i) S=
[
−
√
19
2
,−3
[
∪
]
3,
√
19
2
]
(j) S= R
(k) S= ∅ (l) S=[2, 7]
(m) S=[−2, 2] (n) S=] −∞, 0] ∪ [ 5
2
,∞[
(o) S=]4, 8[ (p) S=
]
−∞,− 1
2
]
∪
[
5
3
,∞[
(q) S=
]
−∞,−2√2[ ∪ ]2√2,∞[ (r) S=] −∞,−4[ ∪ ] − 3, 3[
(s) S=]14,∞[ (t) S=] −∞,−4] ∪ ]1, 2]
(u) S=] − 1, 0[ ∪
]
1
2
, 1
[
(v) S=
]
− 11, 2
3
[
∪ ]3,∞[
(w) S=
]
−∞,−√2[ ∪ ] − 1, 0[ ∪ ]1,√2[ (x) S=] −∞,−1[ ∪ [2, 3[
(y) S=] −∞,−1] ∪ [2, 4] ∪ [6,∞[ (z) S=[−1,∞[
5. Resoluc¸a˜o:
(a) S= ∅ (b) S=
]
− 1, 3
2
[
6. Resoluc¸a˜o:
(a) S=
{
1,− 1
5
}
(b) S=
{
1
2
}
(c) S=
{
−1, 3
2
}
(d) S=
{
1, 3
5
}
(e) S=] − 2, 1[ (f) S=
]
−∞, 1
5
]
∪ [1,∞[
(g) S=] −∞,−1[ (h) S= ∅ (i) S=] −∞, 1[
(j) S=
]
−∞, 5
4
]
(k) S=
]
−∞,− 1
3
[
(l) S=] −∞, 1[ ∪ ]2,∞[
(m) S=
{
7
4
}
(n) S=
{
4
19
, 4
21
}
(o) S=
[
6
11
, 2
3
[
∪
]
2
3
, 10
13
]
Instituto de Matema´tica Universidade Federal de Mato Grosso do Sul