.RPSHWHQVL .KXVXVlearning.upnyk.ac.id/pluginfile.php/12099/mod_resource/content/1... · 6lvwhp...
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Sistem Informasi - UPN[V]Yk 1
Kalkulus (1240033)
Pertemuan Ke-10 BAB V Turunan
Juwairiah, S.Si,M.T
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2
Sub Pokok Bahasan Turunan Fungsi Tingkat Tinggi Teorema L’Hospital
Sistem Informasi - UPN[V]Yk
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Sistem Informasi - UPN[V]Yk 3
Kompetensi Khusus Mahasiswa mampu menyelesaikan
berbagai turunan fungsi
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Sistem Informasi - UPN[V]Yk 4
TURUNAN FUNGSI TINGKAT TINGGI Diberikan fungsi
-Turunan ke – 1 :
-Turunan ke – 2 :
-Turunan ke – 3 : =
-Turunan ke – n :
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Sistem Informasi - UPN[V]Yk 5
Contoh : 1) f (x) = 4x3 -5x2
f ’(x) = 12x2 - 10x
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Sistem Informasi - UPN[V]Yk 6
2) Tentukan turunan ke-4 dari :
Jawab :
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Sistem Informasi - UPN[V]Yk 7
3) Tentukan dari
Jawab :
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Sistem Informasi - UPN[V]Yk 8
4) Carilah rumus umum turunan ke – n dari fungsi
Jawab :
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Sistem Informasi - UPN[V]Yk 9
: :
5) Carilah rumus umum turunan ke – n dari fungsi
Jawab :
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Sistem Informasi - UPN[V]Yk 10
5) Carilah rumus umum turunan ke – n dari fungsi
Jawab :
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Sistem Informasi - UPN[V]Yk 11
TEOREMA L’HOSPITAL
Jika bentuk
Contoh :
1)
2)
Teorema L’Hospital adalah cara untuk menyelesaikan limit dengan menggunakan turunan
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Sistem Informasi - UPN[V]Yk 12
=
=
=
=
Contoh :
3)
Jawab :
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Soal
1. మ 5. ೣ
2. 6.
3. 7. మ
8.
Sistem Informasi - UPN[V]Yk 13
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Sistem Informasi - UPN[V]Yk 14
Referensi Purcell, Varberg, Kalkulus dan Geometri
Analitis, Penerbit Erlangga, 1993 Frank Ayres, Calculus, Mc.Graw Hill, New
York, 1972 J.Salas and Hill, Calculus One and Several
Variables, John Willey& Sons, NewYork, 1982