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Aplicas funciones periódicas
227
x
0
x
1
x
2
x
3
x
4
f
(
x
)
= 3 sen x
f
(
x
)
= sen x
Ejemplo 2:
&QDbLjD#h#FRQVWUXhH#bD#JUi¿FD#GH#bD#IXQFLyQ#
+,
4 sen
4
fx
x
S
§·
!0
.
¨¸
©¹
Solución:
*RPLQLR>#*RPb#!#+í¤/#¤,
YDQJR>#YDQJRb#!##
[
3#
í
#_7_/#3#.#_7_
] = [
í7
,
7
]
EQWHUVHFFLyQ#FRQ#Hf#HdH#`>#
+,
2
x0
,y 4s
e
n
0 4
22
, 0
,22
42
S
§·
§·
!!
0
¤
.
!
0
!
0
0
¨¸
¨¸
¨¸
©¹
©¹
EQWHUVHFFLRQHV#FRQ#Hf#HdH#^>#ThHGHQ#GHWHUPLQDUVH#GHVShpV#GH#WUDlDU#fD#JUm¿FD1
ThQWRV#Pm[LPRV>#ShHGHQ#GHWHUPLQDUVH#GHVShpV#GH#WUDlDU#fD#JUm¿FD1
)DfFhfDPRV#fRV#ShQWRV#SULQFLSDfHV#GH#fD#JUm¿FD>
0
c0
x0
b1
!0 !0 !
1
x
2
S
!
x
S
!
2
3
3
x
2
S
!
4
x2
S
!
*DGR#ghH#D#!#6/#WUDlDPRV#fD#JUm¿FD#VHQRLGDf#VLQ#GHVSfDlDPLHQWRV#k#DfDUJDGD#iHUWLFDf
-
PHQWH>
EQWHUVHFFLRQHV#FRQ#Hf#HdH#^>#
x
, 3, 2, ,
0
,,
2,
SS
S
S
S
!
000
!!
ThQWRV#Pm[LPRV>#
2n
x
2 n, n
, 2, 1,0,1,2,
212
SSS
S
!.
!.
! 00
!!
ThQWRV#PtQLPRV>#
32
n
3
x
2 n, n
, 2, 1,0,1,2,
212
SS
S
S
!.
!.
!0
0
!!
Continúa.
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