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Soal 1.
Penyelesaian analitis :
Hitunglah y pada saat x = 5
Jawaban : Jika diintegralkan menjadi:
(3y - 5) (1+X2)3/2 - 2*(2)^1/2 =
dy/d! = 5! - 3!y
1 + !2
"#al$eak
y ! %(!)
&et#de '' 1,3. 5 -1223'-13
0= 5
r ! y dy/d!=% (!y)
1 2 -5
1 15 15 -1153.,15 naliti4 1,3.2.
2 2 1,23. -3,23.
3 25 1,,23 -1,1, Jadi y(5)= 1,,32,31
3 1,1,1. -5,233
5 35 1,,3 -215.51
, 1,,.311 -11,,32 "alat 3.15
5 1,,31 -,5.5
. 5 1,,33 -1..25
&et#de 6"' 78tta
9' 1 9' 2
0 = 5
r Xr ;r dy/d!=% (!y) 0 =
1 2 -5
1 15 15 -1153.,15 r
2 2 1,23. -3,23.
3 25 1,,23 -1,1, 1
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3 1,1,1. -5,233 2
5 35 1,,3 -215.51 3
, 1,,.311 -11,,32
5 1,,31 -,5.5 5
. 5 1,,33 -1..25 ,
.
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9' 3
5
Xr 71 72 ;r
1 2 0 = 5
15 -25 -12,231 123.5
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2 2511. -231 15.2. r Xr
25 553 -3 ,..1 1
3 55.3 -2 .,, 1 15
35 53. -12 225, 2 2
5,3 -2,.1 113. 3 25
5 55252 -3225 -.. 3
5 5552 -3,13 -23, 5 35
,
5
. 5
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9'
0 = 2
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71 72 73 ;r r Xr 71
2
-25 1112.5 -25532 235, 1 1,23.
-.33 2252 -3,5,3 312,, 2 33.,15
-...3, 313 -.5,122 3.. 3 5,23
-13,,1 -5.5. 5.215 ,,231
-1.,.. 325., -,,5., ,.112 5 .,153.
-23.33 553. -3.11 ..5,
-23 ,5,,.. -.1151 12233 "< = >?/@
-31. 3,11,5 -.3321 153.5
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72 73 7 ;r
1
1
1
1
1
1
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JAB6
6eraCa 7#mD#nen =
= E * Fa% - G * FaD + ? * (-ra)
E * Fa%2 3 m#l
min m3
, m#l/min
G = dCa/dt = , -2 Fa - Fa2
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1 m3
1
Fa2