matematica, ensino mÉdio limites - … resolvidos, limites 2.pdfpage | 1 matematica, ensino mÉdio...
TRANSCRIPT
Page | 1
MATEMATICA, ENSINO MÉDIO
LIMITES - EXERCICIOS RESOLVIDOS.
MATEMÁTICA
Exercícios Resolvidos De Limites
1.
4
1
)1cos1)(1cos1(
1
)cos1)(cos1()cos1)(cos1(
)cos1)(cos1(
)cos1(
cos1
)cos1()cos1(
)cos1)(cos1(cos1
2
2
2
2
20
22
2
2020
)cos1(
x
n
x
n
x
xx
x
xxxse
xx
xse
xx
xxLim
x
x
xx
xxLim
xLim
x
xx
2.
2
1
)cos1()cos1(
)cos1)(cos1(cos1
0
0cos12
2
2200
x
xse
x
xxxLim
x
xLim
x
n
xxxx
3.
2
2
4cos
coscos
cos)(cos
cos
cos
cos
cos1
cos
0
0
1
cos
4
44
x
xx
Lim
xsenxx
xsenxx
x
senxx
xsenx
x
senx
xsenxLim
tgx
xsenxLim
4.
201
2
1
2
32
32
3 3
33
x
x
x
x
x
x
xx
x
Limxx
xLim
xx
5.
Page | 2
21
2
2
1
)1)(2(
)1)(1(
0
0
23
1
12
2
1
x
x
xx
xxLim
xLim
xx x
x
6.
12
12
)11(
11
)11(
)11(
)11()11(
0
011
)1()1(22
00
x
x
xxx
xx
xxx
xxx
xxxxLim
x
xxLim
xx
xx
7. 2
2
x
SenxLimX
8. 2
3
2
3
0
xSen
xSenLimX
9. 2
1
1
1
)1(0
012
2
2
2
20
Cosx
xSe
Cosx
xSeCosxLim
x
n
x
n
xX
10. 4
1
)cos1)(cos1()cos1(
1
)cos1(
1
0
012
2
22
2
20
)cos(
xx
xse
x
Cosx
x
CosxLim
x
n
xx
x
xX
11. 5
5
0
x
xTgLimX
12. 2
1
)cos1()cos1(
)cos1)(cos1(cos1
0
0cos12
2
220
x
xse
x
xxx
x
xLim
x
n
xxX
Page | 3
13.
x
senxsenxLimx
11
0 = 0
0
↔ )11(
)11)(11(
0senxsenxx
senxsenxsenxsenxLimx
↔
)11(
)1()1(22
0senxsenxx
Limsenxsenx
x
= )11(
12
senxsenxx
senx
= 1
14.
0
0
cos
37
0
xx
xsenxsenLimx
40cos
14
cos
14
cos
4
0
xx
xsen
xx
xsenLimx
15.
0
0
cos10
x
senxtgxLimx x
senxx
senx
Limx cos1
cos0
= x
x
xsenx
cos1
cos
)cos1(
=
)cos1(cos
)cos1(
xx
xsenx
00
tgxLimx
16. 2
2
cos
cos
cos
cos1
cos
0
0
14
x
senxx
xsenx
x
senx
xsenx
tgx
CosxSenxLimX
17. 4
1
31
21
3
2
3
2
0
x
xsen
x
xx
xsen
x
x
xsenx
xsenxLimX
Page | 4
18.
e
x
senx
xsenx
xsenxLimLim
e
esenxX
XsenxLim
X
X
X
1
0
1)11(
1
01
11)11(01)1(
19.
exxse
xse
xse
x
xsexLimnnLim
en
n
nnex
XXSe
xLimXSe
X
X
2
1
2
2
220
1)cos2(
1
0
2
1
)cos1(
cos11)1cos2(20
2
1)cos2(
20.
ee
ex
x
x
x
xx
xxx
x
xLimLimX
XX
XLim
X
X
X
4
4
)2(3
1
2
14
3
)2(4
)2(3
31)2(1
3
11
3
1
21. 1
3
2
03
02
3
200
0
x
xX
XLim
22. 02
1 1
2
x
X
X
XLim
23. eeaxab
X
baXLim
X
b
X x
abx
x
baxLim X
1111
0
011
24.
0
1
1
6
3
6
3
6
3
6
3
6
6
3
36n
n
n
n
n
n
n
n
Xn
nn
nLimLim
Page | 5
25.
66
2
3
33
3
3
3
33
3 2
3
3
2
3
2n
n
n
n
n
n
n
n
n
n
n
n
nLim
n
nn
26. 4
5
16
25
162
255
162
255
n
n
n
n
n
n
n
nLimn
27.
ee
en
n
Logo
n
n
n
nn
n
nnLim
nn
nLim
n
n
n
4
4
12112
32
12
1:
42
8
12
12412
12
12321
12
32
28.
2
3
11
3
23
23
23
23
23
2323
23
2
22
22
2
n
nn
nn
n
n
n
nn
nnnn
nnLim
n
nn
nnn
n
29.
4
1
1
1
1
4444
44
4
2
4
3
4
3
44
42
44
44
4
3
4
3
44
44
244
3344
24
34
132
3
2
3
2
3
2
3
2
3
3
3
2
3
2
3
22
3
22
n
n
n
n
n
n
n
n
n
n
nn
nn
nn
nn
nLim
Page | 6
30.
21
2
21
11
0
0
23
12
2
1
xx
xx
xLim
xx
X
31.
aaxaxaxx a
ax
x
axax
xaxaxaLim
aX2222233
2
3
111
0
01
32.
03
0
1
2
21
22
0
0
23
42
2
2
x
x
xx
xx
xLim
xx
X
33.
2
1
11
1
11
1
11
11
0
0
1
1
2
1
xx
x
xxxx
xx
x
xLim
xX
34.
2
3
13
0
0
3
342
3
x
xx
x
xLim xX
35.
2
1
1
11
0
012
2
1
x
x
xx
xx
xLim
xx
X
36.
328442
2
422
2
44
2
2
0
0
2
16 2
222224
2
4
x
xxxxx xx
xx
xxxLimX
37.
3
2
42
22
22
4
8:
.26464;:log;623;0
0
4
8
222
22
33
36
6
2
66
364
2
2
2
y
y
ýy
yy
Limnovo
yxxoyxx
xLim
yy
y
y
y
y
y
Y
X
Page | 7
38.
2
3
11
11
1
1
1
1:
111623;1;1;00
0
11
11
2
2
3
36
6
1
66
30
yy
yy
Limnovo
yyyxxx
xLim
y
y
y
y
y
y
Y
X
39.
1ln:log;1
lnln1
ln)(ln1ln
11
11
111
eoXx
xx
Limx
xxLimxxxLim
eee
x
x
x
x
Xx
LimXX
XLim
X
X
X
XX
XX
Teória e Pratica: