Lista 6

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Lista 6 – Funções de Duas e Três Variáveis - Limite 
 
 
1) Calcule cada limite abaixo: 
 
(a) 
2
53
lim
22
22
)0,0(),( 

 yx
yx
yx
 
 
(b) 
yx
yx
e 
 )2ln,0(),(
lim
 
 
(c) 
senxy
y
yx 


1cos
lim
)0,2/(),( 
 
 
(d) 
1lim 22
)4,3(),(


yx
yx
 
 
(e) 
tgyx
yx


seclim
)4/,0(),( 
 
 
(f) 2
)3,2(),(
11
lim 






 yxyx
 
 
(g) 
yx
yx
yx 


22
)1,1(),(
lim
 
 
(h) 
22)1,1,1(),,(
2
lim
zx
yzxy
zyx 


 
 
(i) 







 zyxzyx
111
lim
)4,3,1(),,(
 
 
(j) 
)2cos(lim 2
)3,0,(),,(
xze y
zyx

 
 
 
(k) 
222
)0,2,0(),,(
lnlim zyx
zyx


 
 
(l) 
)seccos(lim 222
)0,3,3(),,(
zyxsen
zyx


 
 
(m) 
)(lim
)2,2/,/1(),,(
xyzarctg
zyx 
 
 
 
Fórmulas úteis: 
ae a ln
, 
10cos 
, 
1)2/( sen
, 
1)4/( tg
, 
))((22 bababa 
, 
1)2cos( 
, 
 
aa cos/1sec 
 
 
 
 
 
 
Respostas 
 
 
1) (a) 
2
5
 (b) 
2
1
 (c) 
2
 (d) 
62
 (e) 1 (f) 
36
1
 (g) 2 (h) 
2
1

 
 
 (i) 
12
19
 (j) 3 (k) 
2ln
 (l) 2 (m) 
4
