Lista Mat

MAT1157 – C´lculo a uma Vari´vel A - 2014.1 a a

PUC-Rio

Lista de Exerc´ ıcios 1
1. Calcule:
(a) 32 − 24 ÷ 4 ÷ 2

(d) 100 − 40 − 100 ÷ 4 + 1

(b) 32 − 24 ÷ (4 ÷ 2)

(e) 100 − (40 − 100 ÷ 4) + 1

(c) (32 − 24) ÷ 4 ÷ 2

(f)

100 − 40 − 100 ÷ (4 + 1)

(g) 100 − 40 − (100 ÷ 4) + 1
2. Coloque os parˆnteses para que as igualdades sejam verdadeiras: e (a) 33 − 10 + 16 = 7
(b) 35 − 22 − 20 − 13 = 20
(c) 2 + 3 + 4 × 4 = 36
(d) 2 + 3 + 4 × 5 = 37
3. Calcule:
(a)

(3, 1)2 + 0, 39
=
42 − 2 × 5, 5

1
(b) (−8)(− 4 ) − (−1, 1)2 =

(c) −3, 8 + (−6)5 ÷ 100 ÷ 4, 8 + 20, 1 =
(d) [100, 1 ÷ (−0, 7)]3 ÷ 100 + 29200 =
2
(e) (− 3 )3 − (− 1 ) + 3 ÷
2
5

(f)
(g)

1
5

3
10

=

1
− [( 1 )2 ÷ 5 ]
5
=
3
1− 2

(7 × 5)20
=
719 (59 )2

(h) 0, 310 × 0, 3−5 × 0, 37 ÷ 0, 310 =
(i)
(j)

√

3−2 =

√
4

(k) −

10−4 =
16 2
+ +
25 5

1
2

−3

−8=

4. Em cada item abaixo, encontre todos os valores de y que satisfazem a equa¸˜o do item: ca (a) 5(2(7 + y) − 8) = 100
(b) [(3, 1 × 5, 2 − 9, 12) ÷ 2 + y] × 4 − 2 = 18
5. Simplifique: x+2 (a) 5x −
3
√
√
3 2 27
+
−
(b)
2
3

3 √
+ 12
4

6. Em cada item abaixo, encontre todas as solu¸˜es da(s) equa¸˜o(˜es) do item: co ca o
(a) 5x =

(c)

(e)

x
2

2x + 5 = y + 10 y−3=x−4 y 2 − 4y + 4
=0
6y 2 − 12y

(g) 3x2 − 18x = 0

(i)

9x2 − 6x + 1 = 9

(k) x3 + x2 + 20 = (x + 4)(x + 5)

(b) 1 −

x+2 x =
3
2

 3y

+ 5x = 4x + y − 6
2
(d)
 1− y+x = x
2
4
(f)

x3 − 25x = 0

(h) 9x2 − 6x + 1 = 0

(j)

9x2 − 6x + 6 = 0

(l)

(x + 3)2 = (2x + 1)2

7. Em cada item abaixo, encontre todos os valores de x que satisfazem a equa¸˜o do item: ca (a) 10x + 100x2 = −2
√
(b) x2 + 9 = x + 2
7x + 3
(c)
=3
7

(f )

2x/3
2
+ 8x =
9
5/4

(g) x2 = 7
(h) x2 + 9 = 0

x2 + 1
2
x−2
(i)
−
=
2−x x x−1 x √ x2 = 5
(j)

1
5
23
(d)
−
=
5 − x x(5 − x)
7x
2x 7x + 3
(e)
·
=3
5
7

8. (a)