CalA_3_13
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Transcript of CalA_3_13
-
170
3.13 EXERCCIO pg. 93
1 - Se ,||57||3)(xx
xxxf
+= calcule:
(a) 224lim
573lim)(lim =
//
=
+=
+++ x
x
xx
xxxf
xxx.
(b) 61
122lim
573lim)(lim =
//
=
+
= x
x
xx
xxxf
xxx.
2 Se 2)2(1)(+
=
xxf , calcule
(a) +=+ 22 )2(1lim
xx. (b) 0)2(
1lim 2 =++ xx.
Nos exerccios 3 a 40 calcule os limites.
3 - +=++
)143(lim 23 xxx
.
4 - 2002412lim 2 =+=
+
xxx.
5 Usando o exemplo 3.12.5(x), vem 0lim1
1lim 22 =/
=
+
+/
t
t
t
ttt
.
6 - 01
1lim 2 =++
t
tt
.
7 - 21
2lim
35232lim 2
2
2
2
==
+
+ t
t
tt
tttt
.
8 - ==
=
+
++++
32
5
2
35
2lim2lim7
232lim xx
x
x
xx
xxx.
9 - +==
=
+
32
5
2
25
3lim3lim2
73lim xx
x
x
xx
xxx.
-
171
10 - 75
75lim
3725lim 3
3
3
3
=
=
+
+ x
x
x
x
xx.
11 - +==++ x
x
x
xx
xx
22
lim13lim .
12 - 01
1031
lim
103
lim103lim32
3
3
32323
3 =
+
=
/+/
=
++
//
++
xxxx
x
x
xx
x
x
xx
x
xxx
xxx.
13 - +=/
=
/
++ t
t
t
ttt
22
lim41lim .
14 - 32
)/1/53()/cos72(lim
153cos72lim
153)cos72(lim 222
2
2
2
2 =+
=
+
=
+
xxsenxx
xxx
senxx
xxx
senxx
xxx
xxx, j que
0lim e 0coslim 2 == x
senx
x
x
xx.
15 - +=
=
++ )/13()/1(lim
131lim
vv
vvv
v
vv
vv.
16 - 11
1
lim1
1lim22
2
2
=
+
+=
+
+++
xx
x
xx
x
x
x
xx.
17 - 11
1
lim1
1
lim1
1lim22
2
2
2
2
=
+
+
+
+
=
+
+
xx
xxx
x
x
xx
x
x
x
xxx.
18 - 0211
11lim11(lim22
2222
=
=
++
++=+
xx
xxxx
xx.
19 - =+
=
+
+=
+ xx
xxx
xx
xxxxxxxx
xxx 1)1(lim
1)1)(1(lim)1(lim
2
22
2
222
-
172
21
1lim
22
2=
+
=
x
x
xx
x
x
x
x.
20 - =+++
++=++
++ xxx
xxxxxx
xx 21232123lim)2123(lim
2
222
+==+++
++=
/+++
++=
+
///
+ 01
0000001lim
2123
12
lim
243424
2
222
2
xx
x
x
xx
x
x
x
xx
x
x
x
.
21 - 3
103
10lim13
4310lim 22
2
2
==
+++ x
x
x
xx
xx.
22 - ==
+ 2
3
2
3
lim1
12limx
x
x
xx
xx.
23 - 05lim115lim 4
3
34
23
==
++
+/
x
x
xxx
xxx
xx.
24 - 111
7
8
lim7
8lim
22
22=
=
+
=
+
++
ss
s
s
s
s
s
s
ss.
25 - 201
023
72
lim3
72lim22
2
2
=
+
=
+
=
+
xx
x
xx
x
x
x
xx.
26 - xxxxxxxx
xxxxxx 2121516
4121516lim)2121516(lim34
23434
+++
++=++
++
+==
+++
++=
+ 016
2121516
4121516lim
38754
243
xxx
x
xx
xxxxx
.
-
173
27 - 33 77
37
57
23
23lim
1243lim ==+
++ s
s
s
ss
ss.
28 - 23
72lim2
+=+
+ x
x
x.
29 - 21
4010
45
3
lim45
3lim
2
2
2
2
=
+
=
+
=
+
++
yy
y
yy
y
y
yyy
.
30 - 21
45
13
lim45
3lim
2
2=
+
=
+
y
yy
yyy
.
31 - +==
+ + 0
33
lim3 x
x
x
.
32 - ==
03
3lim
3 x
x
x
.
33 - +==
+ + 0
24
lim 22 xx
x
.
34 - ==
02
4lim 22 x
x
x
.
35 - +==
++
+ 012
366lim 26 y
yy
.
36 - ==
+
012
366lim 26 y
yy
.
37 - ==
+ + 01
823lim 24 xx
x
x.
38 - +==
01
823lim 24 xx
x
x.
39 - +==
+ 0
1|3|
1lim3 xx
.
-
174
40 - +==
+ + 0
1|3|
1lim3 xx
.
