More Related Content Similar to limites L´ Hopital resoltos Similar to limites L´ Hopital resoltos (20) limites L´ Hopital resoltos7. ( ) ( )
( )
( ) 8
1
)(cos248
lim
)(24
cos
lim
)2(22
cos
1
lim
2
)ln(
lim
2
0
0
2
2
0
0
2
2
-
=
-
-
=
=
-
=
=
-
=
-
-
--
→
→
→→
xxπsenx
senx
senxxπ
x
xπ
x
senx
xπ
senx
π
x
LH
π
x
OPERO
π
x
LHπ
x
7)
12. ( )
( )
( )
( )
( )
( ) ( )( )
( )
ππ
πxπsen
πxπxxπsen
xπ
xπsenx
xπ
xπsen
xxπtagx
x
LHx
opero
x
def
x
2
)2/(
1
)2/(2/
)2/(2/cos)1(2/1
lim
2/cos
2/)1(
lim
2/cos
2/
)1(lim2/)1(lim
1
0
0
1
11
=
-
-
=
=
-
-+-
=
=
-
=
=-=-
→
→
→→
12)
18. ( )
( ) ( )
( )
( )
0
1
02
lim
1
lim
1
1
1
lim
1
1ln
lim1lnlim
1lnlim1limlnln
11lim
2
0
2
0
2
00
·0
0
log0lim0
0
=
-
=
-
+
=
+-
=
-
-
=
-
=-=
=-=-=
==-
x
xx
xLH
x
x
x
ARRANXO
OPERAC
x
x
xLH
x
xind
x
x
spropiedade
xx
x
spropiedade
xx
x
xx
x
e
exxe
e
ex
x
e
e
x
e
ex
eeA
Ae
→
0
0
→
→
∞
∞
→
∞
→
→→
→
18)
20. ( )
( ) ( )
1
2
0
0
0
0
2
0
2
0
2
0
0
ln
1
0
ln
1
0
ln
1
0
1
1
lim
cos
lim
coslimlim
1
1
lim
ln
cotln
limcotlnlimcotlimlnln
cotlim
-
2
=
-=
+xcos-
=
-
=
=
-
=
-
=-
====
=
eA
xsenxxsen
x
xsen
x
senx
x
xsen
xtagx
x
xsen
tagx
x
gx
gxgxA
Agx
xLHx
simplifico
x
opero
x
opero
x
LHx
x
x
x
x
x
x
→→
→→→
→→→
→
∞
∞
20)
22. ( )
( ) ( )
( )
0
1
coscot
1
lim
cos1
1
·
cot
1
lim
1
cotln
lim
·0
cotlnlim
cotlnlimcotlimlnln
1cotlim
0
2
2
0
00
00
0
0
===
-
-
=
===
===
===
∞
∞
∞
∞
→→
→→
→→
→
xax
xsen
x
xsenax
senx
ax
gxsenx
gxgxA
eAgx
x
simplifico
x
LHxINDx
senx
x
senx
x
senx
x
22)
24. 24)
( )
( ) ( ) 2
2
4
2cos22
cos2
lim
2cos
2
lim
cos2-
lim
22
-
0→
0
0
2
-
0→
0
0
2
-
0→
==
+−
++
=
=
+−
=
+
xxxsenx
xee
xx
senxee
senx
xee
xx
x
LH
xx
xLH
xx
x