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Metode Numerik
Galat (Error)
Kelompok 1
 (200803002) Adisty Putri Inayanti
 (200803004) Annisa Hertyani
 (200803006) Aula Amaliatul Khairo
 (200803008) Darma Wogisfry
 (200803010) Elsa Fadillah Nasution
 (200803012) Fidelia Aprilia Emelia Tamba
 (200803014) Hasanah Dwi Putri Sinaga
 (200803016) Irsyad Baihaqi Lubis
 (200803018) Lenni Rahmayani
Hitung kesalahan yang terjadi dari nilai cos(x) dengan x = 1 apabila
hanya diperhitungkan 5 suku pertama. Nilai sebenarnya dari cos (1) =
0,540302306.
cos 𝑥 = 1 −
𝑥2
2!
+
𝑥4
4!
−
𝑥6
6!
+
𝑥8
8!
− ⋯
Soal :
• Diperhitungkan satu suku pertama
cos 𝑥 = 1 𝜀𝑅 =
0,540302306−1
0,540302306
× 100% = −85,08%
• Diperhitungkan dua suku pertama
cos 𝑥 = 1 −
𝑥2
2!
𝜀𝑅 =
0,540302306−1
0,540302306
× 100% = 7,46%
cos 1 = 1 −
12
2!
𝜀𝑅𝐴 =
0,5−1
0,5
× 100% = −100%
= 1 −
1
2
= 0,5
Penyelesaian :
• Diperhitungkan tiga suku pertama
cos 𝑥 = 1 −
𝑥2
2!
+
𝑥4
4!
𝜀𝑅 =
0,540302306−0,541667
0,540302306
× 100% = −0,2525%
cos 1 = 1 −
12
2!
+
14
4!
𝜀𝑅𝐴 =
0,541667−0,5
0,541667
× 100% = 7,692%
= 1 −
1
2
+
1
24
= 0,541667
Penyelesaian :
• Diperhitungkan empat suku pertama
cos 𝑥 = 1 −
𝑥2
2!
+
𝑥4
4!
−
𝑥6
6!
𝜀𝑅 =
0,540302306−0,5402778
0,540302306
× 100% = 0,0045%
cos 1 = 1 −
12
2!
+
14
4!
−
16
6!
𝜀𝑅𝐴 =
0,5402778 − 0,541667
0,5402778
× 100% = −0,2571%
= 1 −
12
2
+
14
24
−
16
720
= 0,5402778
Penyelesaian :
• Diperhitungkan lima suku pertama
cos 𝑥 = 1 −
𝑥2
2!
+
𝑥4
4!
−
𝑥6
6!
+
𝑥8
8!
𝜀𝑅 =
0,540302306 − 0,5403025794
0,540302306
× 100%
= 0,00005%
cos 1 = 1 −
12
2!
+
14
4!
−
16
6!
+
18
8!
𝜀𝑅𝐴=
0,5403025794 − 0,5402778
0,5403025794
× 100%
= 0.0046%
= 1 −
1
2
+
1
24
−
16
720
+
18
40320
= 0,540302579
Penyelesaian :
Tabel Hasil Perhitungan Galat:
Suku Hasil 𝜀𝑅(%) 𝜀𝑅𝐴(%)
1 1 −85,08 −
2 0,5 7,46 −100
3 0,541667 −0,2525 7,692
4 0,5402778 0,0045 −0,2571
5 0,540302579 0,00005 0.0046
Terimakasih

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PPT KEL.1 METODE NUMERIK.pptx

  • 2. Kelompok 1  (200803002) Adisty Putri Inayanti  (200803004) Annisa Hertyani  (200803006) Aula Amaliatul Khairo  (200803008) Darma Wogisfry  (200803010) Elsa Fadillah Nasution  (200803012) Fidelia Aprilia Emelia Tamba  (200803014) Hasanah Dwi Putri Sinaga  (200803016) Irsyad Baihaqi Lubis  (200803018) Lenni Rahmayani
  • 3. Hitung kesalahan yang terjadi dari nilai cos(x) dengan x = 1 apabila hanya diperhitungkan 5 suku pertama. Nilai sebenarnya dari cos (1) = 0,540302306. cos 𝑥 = 1 − 𝑥2 2! + 𝑥4 4! − 𝑥6 6! + 𝑥8 8! − ⋯ Soal :
  • 4. • Diperhitungkan satu suku pertama cos 𝑥 = 1 𝜀𝑅 = 0,540302306−1 0,540302306 × 100% = −85,08% • Diperhitungkan dua suku pertama cos 𝑥 = 1 − 𝑥2 2! 𝜀𝑅 = 0,540302306−1 0,540302306 × 100% = 7,46% cos 1 = 1 − 12 2! 𝜀𝑅𝐴 = 0,5−1 0,5 × 100% = −100% = 1 − 1 2 = 0,5 Penyelesaian :
  • 5. • Diperhitungkan tiga suku pertama cos 𝑥 = 1 − 𝑥2 2! + 𝑥4 4! 𝜀𝑅 = 0,540302306−0,541667 0,540302306 × 100% = −0,2525% cos 1 = 1 − 12 2! + 14 4! 𝜀𝑅𝐴 = 0,541667−0,5 0,541667 × 100% = 7,692% = 1 − 1 2 + 1 24 = 0,541667 Penyelesaian :
  • 6. • Diperhitungkan empat suku pertama cos 𝑥 = 1 − 𝑥2 2! + 𝑥4 4! − 𝑥6 6! 𝜀𝑅 = 0,540302306−0,5402778 0,540302306 × 100% = 0,0045% cos 1 = 1 − 12 2! + 14 4! − 16 6! 𝜀𝑅𝐴 = 0,5402778 − 0,541667 0,5402778 × 100% = −0,2571% = 1 − 12 2 + 14 24 − 16 720 = 0,5402778 Penyelesaian :
  • 7. • Diperhitungkan lima suku pertama cos 𝑥 = 1 − 𝑥2 2! + 𝑥4 4! − 𝑥6 6! + 𝑥8 8! 𝜀𝑅 = 0,540302306 − 0,5403025794 0,540302306 × 100% = 0,00005% cos 1 = 1 − 12 2! + 14 4! − 16 6! + 18 8! 𝜀𝑅𝐴= 0,5403025794 − 0,5402778 0,5403025794 × 100% = 0.0046% = 1 − 1 2 + 1 24 − 16 720 + 18 40320 = 0,540302579 Penyelesaian :
  • 8. Tabel Hasil Perhitungan Galat: Suku Hasil 𝜀𝑅(%) 𝜀𝑅𝐴(%) 1 1 −85,08 − 2 0,5 7,46 −100 3 0,541667 −0,2525 7,692 4 0,5402778 0,0045 −0,2571 5 0,540302579 0,00005 0.0046