Caderno 1 : Domínios de Definição, Limites e Continuidade

1.3. EXERCÍCIOS PROPOSTOS 7
(c) f (x, y) =log(1− x + y), comx, y ≥ 0
(d) f (x, y) =
(e) f (x, y) =
log (4 − x − y)
4√ xy − 3
1
p 4 − x 2 − y 2
q
(f) f (x, y) =1+ − (x − y) 2
(g) f (x, y) = √ x 2 − 4+ p 4 − y 2
(h) f (x, y) = √ 1 − x 2 + p 1 − y 2
(i) f (x, y) =
(j) f (x, y) =
(k) f (x, y) =
1
x 2 + y 2
1
p y − √ x
x 2 y 2
q
(x 2 + y 2 ) 3
(l) f (x, y) =arcsin y
x
(m) f (x, y) =log ¡ 1 − x 2¢ +cos(xy)
(n) f (x, y) =
µ
x + y
x2 1/2
− y
(o) f (x, y) =
xy
|x| + |y|
(p) f (x, y) = ¡ −x2 − y2 +4 ¢ xy
3. Determine o domínio de definição das seguintes funções:
⎧
1
⎪⎨
log (x + y)
(a) f (x, y) =
⎪⎩ √
1 − x − y
,
,
(x, y) :x + y>0
(x, y) :x + y ≤ 0
⎧
⎪⎨
2x
(b) f (x, y) =
⎪⎩
3 +3y4 2x3 − y3 1
,
,
(x, y) 6= (0, 0)
(x, y) =(0, 0)