lista 1- cálculo ufms

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Ca´lculo I - Lista de Exerc´ıcios no¯ 1 - 1o¯ semestre/2016
1. Represente geometricamente os seguintes conjuntos:
(a) [1, 4] (b) ] −∞, 3[ (c) ]1/2,+∞[ (d) [−5, 1] ∪ [0, 7[
(e) [−5, 1] ∩ [0, 7[ (f) [1, 3]∩]3, 8] (g) [1, 3]∪]4, 7] (h) [−5, 6[∩]0,+∞[
2. Estude o sinal de cada uma das seguintes expresso˜es:
(a) 5− x (b) 3x+ 4 (c)
x+ 2
1− 2x
(d)
(3− x)(4x+ 1)
2x+ 1
(e)
(3+ x)2
2x+ 1
(f) x2 − 4 (g)−x2 + 2x− 3 (h) 9x2 + 12x+ 4
3. Fatore os polinoˆmios abaixo, se poss´ıvel:
(a) x2 − 3x+ 2 (b) −3x2 − 2x+ 1 (c) −2x2 + 5x (d) x2 − x− 1
(e) 4x2 − 4x+ 1 (f) x2 + x+ 10 (g) 6x2 − x− 2 (h) x3 − 1
(i) x3 + 2x2 − x− 2 (j) x4 − x2 − 6 (k) x3 + 2x2 − 3x (l) x3 + 3x2 − 4x− 12
4. Resolva as seguintes inequac¸o˜es:
(a) 4x+ 2 < x− 1 (b) 3x− 2 ≥ 7 (c) x− 3
x+ 2
< 0 (d)
x+ 3
1− 2x
< 0
(e) x(2x− 5) < 0 (f)
2− x
x+ 4
< 3 (g)
2+ x
(x+ 5)2
< 0 (h)
2
x2 + 4
< 0
(i)
1
x2 − 9
≥ 2 (j) x
2 + 8
1+ x2
≥ 1 (k) 1+ x
2
x2 + 8
≥ 1 (l) 3x− 14 ≥ x2 − 6x
(m) x2 ≤ 4 (n) −2x2 + 5x ≤ 0 (o) x
x− 4
> 2 (p) 6x2 − 7x− 2 ≥ 3
(q) x2 > 8 (r)
x2 − 9
x+ 4
< 0 (s)
x2 − 25
x+ 5
> 9 (t)
(x− 2)(x+ 4)
1− x
≥ 0
(u)
x3 − x
2x− 1
< 0 (v)
2
x− 3
>
5
3x− 2
(w)
x(x2 − 2)
x2 − 1
< 0 (x)
2− x
−x2 + 2x+ 3
≤ 0
(y) (x2 − 3x− 4)(x2 − 8x+ 12) ≥ 0 (z) x3 + 2x2 + 3x+ 2 ≥ 0
5. Resolva:
(a) 5x+ 7 ≤ 2− x < 5x− 8 (b) x− 10 < 2− 7x < x+ 10
6. Resolva as equac¸o˜es e inequac¸o˜es modulares:
(a) |5x− 2| = 3 (b) |x| = 3x− 1 (c) |x− 4| = |3x− 2| (d) |2− 3x| = |2x− 1|
(e) |2x+ 1| < 3 (f) |5x− 3| ≥ 2 (g) |x+ 3| − |1− x| < 0 (h) |2x+ 1| < x− 1
(i) |x− 3| > x+ 1 (j) |2x| ≤ |5− 2x| (k) |x− 1| − |x+ 2| > x (l) |x− 2| + |x− 1| > 1
(m)
∣∣∣∣2x− 1x− 3
∣∣∣∣ = 2 (n) ∣∣∣∣ x1− 5x
∣∣∣∣ = 4 (o) ∣∣∣∣ x− 22− 3x
∣∣∣∣ ≥ 4
Instituto de Matema´tica Universidade Federal de Mato Grosso do Sul