Roboguru
SD

Jika f(t)=cos2 (2t+2π​), maka f  (6π​)=....

Pertanyaan

Jika begin mathsize 14px style straight f left parenthesis straight t right parenthesis equals cos squared space open parentheses 2 straight t plus straight pi over 2 close parentheses end style, maka begin mathsize 14px style straight f to the power of apostrophe apostrophe end exponent open parentheses straight pi over 6 close parentheses equals end style....

  1. begin mathsize 14px style negative 4 square root of 3 end style 

  2. begin mathsize 14px style negative 4 end style 

  3. begin mathsize 14px style 0 end style 

  4. begin mathsize 14px style 4 end style 

  5. begin mathsize 14px style 4 square root of 3 end style 

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Diketahui undefined, maka untuk mencari turunannya kita gunakan aturan rantai.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f to the power of apostrophe left parenthesis straight t right parenthesis end cell equals cell 2 space cos space open parentheses 2 straight t plus straight pi over 2 close parentheses open parentheses negative sin space open parentheses 2 straight t plus straight pi over 2 close parentheses close parentheses left parenthesis 2 right parenthesis end cell row cell straight f to the power of apostrophe left parenthesis straight t right parenthesis end cell equals cell negative 2 left parenthesis 2 left parenthesis sin space open parentheses 2 straight t plus straight pi over 2 close parentheses space cos space open parentheses 2 straight t plus straight pi over 2 close parentheses end cell row cell straight f to the power of apostrophe left parenthesis straight t right parenthesis end cell equals cell negative 2 space sin space 2 open parentheses 2 straight t plus straight pi over 2 close parentheses end cell row cell straight f to the power of apostrophe left parenthesis straight t right parenthesis end cell equals cell negative 2 space sin space left parenthesis 4 straight t plus straight pi right parenthesis end cell end table end style 

Kemudian cari turunan kedua f(t).

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight f apostrophe apostrophe left parenthesis straight t right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 2 left parenthesis 4 right parenthesis space cos space left parenthesis 4 straight t plus straight pi right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight f apostrophe apostrophe left parenthesis straight t right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 8 space cos space left parenthesis 4 straight t plus straight pi right parenthesis end cell end table end style 

Substitusi begin mathsize 14px style straight t equals straight pi over 6 end style, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f apostrophe apostrophe open parentheses straight pi over 6 close parentheses end cell equals cell negative 8 space cos space open parentheses 4 open parentheses straight pi over 6 close parentheses plus straight pi close parentheses end cell row blank equals cell negative 8 space cos space open parentheses 5 over 3 straight pi close parentheses end cell row blank equals cell negative 8 open parentheses 1 half close parentheses end cell row blank equals cell negative 4   end cell end table end style 

Jadi, jawaban yang tepat adalah B.

65

0.0 (0 rating)

Pertanyaan serupa

Jika f(t)=sin3 4t−(4t2−2t+4),  maka nilai dari f  (12π​) adalah ....

80

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia