Exercicios Revisão matematica

Cálculo I

Lista de Exercícios 1
2° semestre de 2014 – Prof. Claudio H. Asano

1

Revisão de Álgebra

1.1 Complete usando a propriedade especificada:
(a) 13 + 32 =

(comutativa).

(f) 23 · 31 =

(comutativa).

(b) 7 + (6 + 3) =

(associativa).

(g) (12 · 34) · 5 =

(associativa).

(c) 5 + 0 =

(elemento neutro).

(h) 7 · 1 =

(elemento neutro).

(d) 3 + (−3) =

(elemento oposto).

(i) 5 ·

1
=
5

(elemento inverso).

(e) 7(3 + 2) =

(distributiva).

(j) (9 + 7) · 4 =

1.2 Calcule:
(a) 2 · 3 + 5

(h) 1/3 − 3

Resp: −8/3

Resp: 11

(b) 2 + 3 · 5

(i) 1/2 · 4 − 1
Resp: 1

Resp: 17

1
(c) 2 · − 3
3
7
Resp: − 3

2
(j) 3
4
5
Resp:

(k)

(e) 1/2 − 1/3
(l)
Resp: 4/3

(g) 1 − 1/3
Resp: 2/3

3

·

5
6

4
5
6

Resp: 4/5

Resp: 1/6

(f) 1 + 1/3

2
4

2
4
3

Resp: −

·

4
5

6

Resp: 1/5

1 3
−
(m) 2 4
4 2
+
3 5

15
104

2 1
−
(n) 7 4
5 3
·
2 4
Resp:

(d) 1/2 + 1/3
Resp: 5/6

(distributiva).

2
105

(o) 2 5/2 + 2/3)2
Resp: 361/18

(p) (2/3 − 1/2)−2
Resp: 36
3)

(q) 3(2

Resp: 6561

(r) (32 )3
Resp: 729

1.3 Expanda as expressões abaixo:
(a) a(b + 2c)

(f)

Resp: ab + 2ac

Resp:

(b) (b − c)a

Resp: ab − ac

Resp:

− ab −

1−a−b a+b (g) (a − b)2

(c) (a + b)(a − 2b) a2 1
−1
a+b

2b2

(d) (2a − b)(3a − c)
Resp: 6a2 − 3ab −
2ac + bc

(e) (x + y + z)(x + y)
Resp: x2 + 2xy + xz + y 2 + yz

1.4 Fatore as expressões abaixo:
(a) a2 − 2a
Resp: a(a − 2)

(b) a2 − 16
Resp: (a + 4)(a − 4)

Resp: a2 − 2ab + b2

(h) (a − 2b)3
Resp: a3 − 6a2 b +
12ab2 − 8b3

(i) (a − b)4
Resp: a4 − 4a3 b +
6a2 b2 − 4ab3 + b4

(c) a2 + 2a + 1
Resp: (a + 1)2

(d) a2 − 6a + 9
Resp: (a − 3)2

(j)

a+2 a−b Resp:

2

a2 + 4a + 4 a2 − 2ab + b2

(k) (a + b)2 (a − b)2
Resp: a4 − 2a2 b2 + b4

(l) (a + b)−2 + (a − b)−1
Resp:
a2 + 2ab + b2 + a − b a3 + a2 b − ab2 − b3

(m) (a +