DIFERENSIAL PARSIAL
1. Tentukan fx, fy, fxy, fxyx
a. f( x,y) = 3x2 . sin y2
jawab :
f( x,y) =
misal : u = 3x2
u’ = 6x
v = sin y2
v = 0
fx(x,y) = u’ . v + u . v’
= 6x . sin y2 + 3x2 . 0
= 6x sin y2
Fy(x,y) =
Misal : u = 3x2
u’ = 0
v = sin y2
v’ = 2 y cos y2
fy(x,y) = u’ . v + u . v’
= 0 . sin y2 + 3 x2 . 2y cos y2
= 6 x2y . cos y2
Fxy(x,y) =
Misal : u = 6x
u’ = 0
v = sin y2
v’ = 2 y cos y2
fy(x,y) = u’ . v + u . v’
= 0 . sin y2 + 3 x2 . 2y cos y2
= 6 x2y . cos y2
Fxyx(x,y) =
Misal : u = 12xy
u’ = 12
v = cos y2
v’ = -2 y sin y2
fy(x,y) = u’ . v + u . v’
= 12y . cos y2 + 12 xy . (- 2y sin y2)
= 12y cos y2 – cos y x y2 . sin y2
b. f( x,y) = x2 .
Jawab :
f( x,y) =
misal : u = x2
u’ = 2x
v =
v =
fx(x,y) = u’ . v + u . v’
= 2x . + x2 .
= 2x . +
2. Jika f ( x,y) = x2 - 3xy + 2y – 3y + 5
a. Hitung
fx (2,3) = 2x – 3y + 2
= 2 (2) – 3 (3) + 2
= -3
b. Hitung
fy (2,3) = -3x – 3
= -3 ( 9 ) – 3
= -9
3.
Tentukan
a. ft( t = x ) =
misal : u = t x
u’ = -2 x sin 2 t x
v = t2 + x2
v = 2t
fx(x,y) =
=
=
=
b. fx( t = x ) =
misal : u = t x
u’ = -2 x sin 2 t x
v = t2 + x2
v = 2x
fx(x,y) =
=
=
=
30 maret 2010
INTEGRAL PANGKAT
a. =
=
=
=
= y
= ( y2 – y1 )
= (4 – 2)
= 2
b. =
=
=
=
=
=
=
=
=
c. . =
=
=
=
=
=
=
=
=
=
=
INTEGTAL GARIS
1. Hitung melalui persamaan garis dari (0,1) ke (1,2)
Jawab :
y - 1 = x
y = x + 1
ó
ó
ó
ó +
ó( + { (
ó( - - 1 ) + ( + 2 – 2 ) – ( + - 1 )
ó( + - 1 ) + - + 1 )
ó - 1
ó
2. Hitung disepanjang x = t dan y = t2 + 1
x = t y = t2 + 1
x1 = 0 ¦t1 = 0 y1= 1 ¦t1 = 0
x2 = 1 ¦t2 = 1 y2= 2 ¦t2 = 1
ó
ó
ó
ó (
ó -1
ó
SISTEM KOORDINAT
