Calculo II
1
&¨/&8/2,, ( exemplo 5 - página 3 - texto 1 sobre Diferenciais ) y = f(x) = , ⋅ + - ⋅ 7 x arcsen 2 49 x 49 2 x V 2 U y ’ = ( ) ( ) 7 1 7 x 1 1 2 49 x 2 x 49 2 1 2 x x 49 2 1 dx dy 2 2 1 2 2 ⋅ - ⋅ + - ⋅ - ⋅ ⋅ + - ⋅ = - ( ) 49 x 1 1 2 7 x 49 2 x x 49 2 1 dx dy 2 2 1 2 2 2 - ⋅ + - ⋅ - - ⋅ = 49 x 49 1 2 7 x 49 2 x x 49 2 1 dx dy 2 2 2 2 - ⋅ + - ⋅ - - ⋅ = 7 x 49 1 2 7 x 49 2 x x 49 2 1 dx dy 2 2 2 2 - ⋅ + - ⋅ - - ⋅ = 2 2 2 2 x 49 7 2 7 x 49 2 x x 49 2 1 dx dy - ⋅ + - ⋅ - - ⋅ = 2 2 2 x 49 2 x 49 x 49 2 1 dx dy - ⋅ - + - ⋅ = e racionalizando: 2 2 2 2 2 x 49 x 49 x 49 2 x 49 x 49 2 1 dx dy - - ⋅ - ⋅ - + - ⋅ = ( ) ( ) 2 2 2 2 x 49 2 x 49 x 49 x 49 2 1 dx dy - ⋅ - ⋅ - + - ⋅ = 2 2 x 49 2 1 x 49 2 1 dx dy - ⋅ + - ⋅ = 2 x 49 dx dy - =
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Exemplos de Calculo II
Transcript of Calculo II
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&/&8/2,, ( exemplo 5 pgina 3 texto 1 sobre Diferenciais )
y = f(x) = ,
+
7x
arcsen2
49x49
2x
V
2
U
y = ( ) ( )71
7x1
12
49x2x49
21
2x
x4921
dxdy
22
122
++=
( )49x1
127
x492
xx49
21
dxdy
2212
22
+
=
49x49
127
x492x
x4921
dxdy
22
22
+
=
7x49
127
x492x
x4921
dxdy
22
22
+
=
22
22
x497
27
x492x
x4921
dxdy
+
=
2
22
x492x49
x4921
dxdy
+= e racionalizando:
2
2
2
22
x49
x49
x492
x49x49
21
dxdy
+=
( )( )222
2
x492x49x49
x4921
dxdy
+=
22 x4921
x4921
dxdy
+=
2x49dxdy
=
