Lista4-gabarito

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MAW 117-Introdução ao cálculo-2015/1
Gabarito-Lista 4
1. (a) y > 0 para x ∈ (−3,−2) ∪ (−1, 1);
y < 0 para x ∈ (−∞,−3) ∪ (−2,−1) ∪ (1,+∞)
(b) y > 0 para x ∈ (−∞,−7) ∪ (−2, 0) ∪ (4,+∞);
y < 0 para x ∈ (−7,−2) ∪ (0, 4)
(c) y > 0 para x ∈ (−5,−4) ∪ (−1,√2) ∪ (e, 3) ∪ (pi,+∞);
y < 0 para x ∈ (−∞,−5) ∪ (−4,−1) ∪ (√2, e) ∪ (3, pi)
2. (a) ma =
2
3
(b) mb = −3
2
(c) mc = −5
3
mc < mb < ma
3. (a) x− 6y + 23 = 0
(b) 6x+ 7y + 9 = 0
(c) 9x− 2y + 51 = 0
4. (a) (−3
2
,−5
2
) e (1, 0)
(b) (−1,−2) e (1, 0)
5. (a)
√
29
(b)
√
793
3
(c)
√
16 + (6− pi)2
6. (a) a = −6 e a = 2
(b) a ∈ (−∞,−3
2
)
(c) a ∈ (−∞, 7
2
]
7. (a) (−∞, 1
2
(−1−√5)) ∪ (1
2
(
√
5− 1),+∞)
(b)
8. (a) x = pi −√3 ou x = √3 + pi
(b) x =
3
2
(c) x = 0 ou x = 3
1
(d) x = 1 ou x = 3
(e) x = 1
3
(1− 2√13); x = 1
3
(1 + 2
√
13); 1
3
(1−√46) ou 1
3
(1 +
√
46)
9. (a) x ∈ [−11, 3]
(b) x ∈ (−∞, pi −√3] ∪ [√3 + pi,+∞)
(c) x ∈ (−∞, 3
2
]
(d) x ∈ (−∞, 0] ∪ [3,+∞)
(e) x ∈ (1, 3)
(f) x ∈ (−∞, 1
3
(1− 2√13)) ∪ (1
3
(1−√46), 1
3
(1 +
√
46)) ∪ (1
3
(1 + 2
√
13),+∞)
(g) x ∈ (1
4
(3−√65), 1
4
(3−√33)) ∪ (1
4
(3 +
√
33), 1
4
(3 +
√
65))
(h) x ∈ (−∞,−8
5
) ∪ (−8
5
, 1
56
(−1−√6161)] ∪ [ 1
56
(
√
6161− 1,+∞))
2