1 Lista Mat Aplic COMEX

1a Lista de Matem´atica Aplicada - Fun¸co˜es
Prof. S´avio Mendes Fran¸ca
1. Utilizando uma calculadora cient´ıfica, calcule: (escreva todas as casas decimais do visor da calculadora)
(a) 25
(b) 34
(c) 2−3
(d) 3−2
(e)

1
2

(f)

1
2

5

2
3

(g) log 3 5
(dica: use a f´ ormula da mudan¸ca de base)
√
(h) log 13 5
(i) sen 30◦

(dica: pase a calculadora para a fun¸c˜ao DEG)

(j) sen 0, 5

(dica: pase a calculadora para a fun¸c˜ao RAD)

(k) cos 25◦
(l) cos − 2
(m) tg -50◦
(n) tg 0, 4

2. Resolva as inequa¸c˜ oes abaixo:
(a) 2x − 2 < 0
(b) 4x − 8 ≥ 0
(c) −2x + 6 ≤ 0
(d) −3x − 6 > 0
(e) 2x − 6 < 0
(f) x2 − x − 2 ≥ 0
(g) x2 + 3x − 4 > 0
(h) −x2 + 2x + 3 ≤ 0
(i) −x2 − 5x − 4 ≥ 0
(j) 2x2 − x − 1 ≤ 0

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3. Resolva as inequa¸c˜ oes abaixo:
(a) (2x − 2) . x2 − 9 < 0
(b) (4x − 8) . (3x − 3) ≥ 0
(c) x2 − x − 2 . x2 − 9 ≥ 0
(d) x2 + 3x − 4 . x2 − 3x > 0
3x − 6
≤0
x2 − 9 x2 + 5x + 4
>0
(f)
2x + 4 x2 + 2x − 3
(g) 2
≤0
x − 5x + 4 x2 − 5x
(h) 2
>0
x −4
(e)

4. Sabendo que a ´e uma raiz do polinˆ omio p, fatore o polinˆomio p na forma (x − a) .q (x) nos casos abaixo: (a) p (x) = x3 − 2x2 + 3x − 2 e a = 1
(b) p (x) = x4 + x3 + x2 + x − 4 e a = 1
(c) p (x) = x3 + x2 − 8x + 4 e a = 2
(d) p (x) = x2 − x − 2 e a = 2
(e) p (x) = x2 − 4 e a = 2
(f) p (x) = x3 − 27 e a = 3
(g) p (x) = x4 − x2 − 6x e a = 2
(h) p (x) = x3 − 8 e a = 2
(i) p (x) = x2 − 2x + 1 e a = 1
(j) p (x) = x3 − 2x2 − 4x + 3 e a = 3
(k) p (x) = x3 − 1 e a = 1
(l) p (x) = x2 − 5x + 4 e a = 1
(m) p (x) = x3 − 3x2 + 4 e a = 2
(n) p (x) = x4 + x3 + 2x2 − 5x + 1 e a = 1
(o) p (x) = x5 − x3 + 4x2 − 6x + 4 e a = 2
(p) p (x) = x2 − 16 e a = 4
(q) p (x) = x2 − 3x − 10 e a = 5
(r) p (x) = x5 + x2 − 3x + 1 e a = 1
(s) p (x) = x3 + x2 + x − 14 e a = 2
(t) p (x) = x3 − 4x2 + 2x + 3 e a = 3

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