1 / 16

SELAMAT DATANG PADA SEMINAR

SELAMAT DATANG PADA SEMINAR. TURUNAN DAN FUNGSI. OLEH KELOMPOK VI. ATURAN PENCARIAN TURUNAN. Aturan rantai : Turunan fungsi trigonometri : f(x) = sin x  f’(x)= cos x f(x) = cos x  f’(x)= -sin x f(x) = tan x  f’(x)= sec 2 x. ATURAN PENCARIAN TURUNAN. Jika maka :

gomer
Download Presentation

SELAMAT DATANG PADA SEMINAR

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SELAMAT DATANG PADA SEMINAR TURUNAN DAN FUNGSI OLEH KELOMPOK VI

  2. ATURAN PENCARIAN TURUNAN Aturan rantai : Turunan fungsi trigonometri : • f(x) = sin x  f’(x)= cos x • f(x) = cos x  f’(x)= -sin x • f(x) = tan x  f’(x)= sec2 x

  3. ATURAN PENCARIAN TURUNAN Jika maka : Jika maka :

  4. Contoh : • f(x) = sin(x2+3x) • f(x) = tan2(x2+3x) • f(x) = (x3+2x2+4x+5)3 • f(x) = sin2x+2sin x • f(x) = sin2x . cos 3x • f(x) =

  5. JENIS-JENIS FUNGSI Fungsi Genap Jika f(x) = f(-x)  simetris terhadap sumbu y Contoh : f(x) = x2 f(-x) = (-x)2 = x2 Artinya f(x) = x2 adalah fungsi genap

  6. JENIS-JENIS FUNGSI Fungsi Ganjil Jika f(-x) = -f(x)  simetris terhadap titik asal Contoh : f(x) = sin x f(-x) = sin(-x) = -sin x Artinya f(x) = sin x adalah fungsi ganjil

  7. JENIS-JENIS FUNGSI Fungsi Nilai Mutlak Contoh : f(x) = x – 2 x – 2 untuk x > 2 -x + 2 untuk x < 2

  8. JENIS-JENIS FUNGSI Contoh : Tentukan jenis fungsi f(x) = tan x f(x) = x3 Gambarkan grafik fungsi f(x) =2x – 3 Tunjukkan jika x< 2 maka :

  9. KOMPOSISI FUNGSI Contoh : f(x) = 2x g(x) = x2 + 3x + 2 Tentukan (g o f)(x) (f o g)(x)

  10. KOMPOSISI FUNGSI f(x) = 2x g(x) = x2 + 3x + 2 (g o f)(x) = g(f(x)) g(2x) = (2x)2 + 3(2x) + 2 = 4x2 + 6x + 2 (f o g)(x) = f(g(x)) f(x2 + 3x + 2) = 2(x2 + 3x + 2) = 2x2 + 6x + 4

  11. FUNGSI TRIGONOMETRI Jenis-jenis fungsi trigonometri : * sin x * cosec x * cos x * sec x * tan x * cotan x Sifat-sifat : sin2x + cos2x = 1 sin(-x) = -sin(x) dan cos(-x) = cos(x) sin 2x = 2.sin x. cos x

  12. FUNGSI TRIGONOMETRI Contoh : Buktikan bahwa cosec 2x = ½ . cosec x . sec x cotan x = cos x . cosec x tan x = sin x . sec x

  13. LIMIT Jika : n  bilangan bulat positif, c dan k  suatu konstanta f dan g  fungsi Maka :

  14. LIMIT Contoh : Tentukan nilai limit berikut

  15. KEKONTINUAN FUNGSI Suatu fungsi kontinu di x = a jika : Contoh : Tentukan nilai f(2) agar f(x) kontinu di x=2

  16. TERIMA KASIH WASSALAM

More Related