Me podrian dar unos ejemplos de límites trigonometricos que esten sencillos y que utilicen las identidades trigonometricas
Observe:
Vou apresentar só uno exemplo, ok ?
lim...( 1 - cos x )/x
x->0
( 1 - cos x ).( 1 + cos x )
------------------------------------ =
.....x.( 1 + cos x )
1 - cos² x
------------------ =
x(1+cos x )
Como sen² x = 1 - cos² x,temos:
.....sen² x
-------------------- =
x( 1 + cos x )
sen x .. *.....sen x
--------........---------------
...x......... 1 + cos x
Logo, temos:
lim....sen x.....lim....sen x
x->0.---------- * x->0.------------ =
...........x...............1 + cos x
Lembrando que :
lim....( sen x )/x = 1
1 . ( sen 0 )/( 1 + cos 0 ) =
1 . 0/( 1 + 1 ) =
1 . 0/2 =
1 . 0 =
R =======> 0
Good Luck!
Teresina-Piauí , 15/08/2008
Hora 16: 00
Temperatura 32º
Abraços!!!!!!!!!!
Fonte(s):
Minha
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…….*-,…….`*-,...`~,..``.,,,-*……….|.,*....
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Comments
Observe:
Vou apresentar só uno exemplo, ok ?
lim...( 1 - cos x )/x
x->0
( 1 - cos x ).( 1 + cos x )
------------------------------------ =
.....x.( 1 + cos x )
1 - cos² x
------------------ =
x(1+cos x )
Como sen² x = 1 - cos² x,temos:
.....sen² x
-------------------- =
x( 1 + cos x )
sen x .. *.....sen x
--------........---------------
...x......... 1 + cos x
Logo, temos:
lim....sen x.....lim....sen x
x->0.---------- * x->0.------------ =
...........x...............1 + cos x
Lembrando que :
lim....( sen x )/x = 1
x->0
1 . ( sen 0 )/( 1 + cos 0 ) =
1 . 0/( 1 + 1 ) =
1 . 0/2 =
1 . 0 =
R =======> 0
Good Luck!
Teresina-Piauí , 15/08/2008
Hora 16: 00
Temperatura 32º
Abraços!!!!!!!!!!
Fonte(s):
Minha
………………..,-~*’`¯lllllll`*~,
…………..,-~*`lllllllllllllllllllllllllll...
………,-~*lllllllllllllllllllllllllllllll...
……,-*lllllllllllllllllllllllllllllllll...
….;*`lllllllllllllllllllllllllll,-~*~-...
…..\lllllllllllllllllllllllllll/………\;;...
…...\lllllllllllllllllllll,-*………..`~-~...
…….\llllllllllll,-~*…………………)_-\..*`*;....
……..\,-*`¯,*`)…………,-~*`~.………….../
……...|/.../…/~,…...-~*,-~*`;……………./.\
……../.../…/…/..,-,..*~,.`*~*…………….*......
…….|.../…/…/.*`...\...……………………)….)¯`~,
…….|./…/…./…….)……,.)`*~-,……….../….|..)...
……/./.../…,*`-,…..`-,…*`….,---…...\…./...
…...(……….)`*~-,….`*`.,-~*.,-*……|…/.…/…...
…….*-,…….`*-,...`~,..``.,,,-*……….|.,*....
……….*,………`-,…)-,…………..,-*`...,-*….(`-,...
..............f`-,………`-,/…*-,___,,-~*…...