Roboguru

Nilai dari  = ....

Nilai dari limit as x rightwards arrow 0 of fraction numerator sin open parentheses 8 x close parentheses plus sin open parentheses 4 x close parentheses over denominator 2 x left parenthesis cos open parentheses 12 x close parentheses plus cos open parentheses 8 x close parentheses right parenthesis end fraction = ....

  1. negative sign 3

  2. negative sign 3 over 10

  3. 1 fifth

  4. 3 over 10

  5. 3

Jawaban:

Dapat dilihat dari gambar bahwa ketiga sudut tersebut merupakan sudut berpelurus, sehingga :

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin open parentheses 8 x close parentheses plus sin open parentheses 4 x close parentheses over denominator 2 x left parenthesis cos open parentheses 12 x close parentheses plus cos open parentheses 8 x close parentheses right parenthesis end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator 2 cross times sin open parentheses begin display style fraction numerator 8 x plus 4 x over denominator 2 end fraction end style close parentheses cross times cos open parentheses begin display style fraction numerator 8 x minus 4 x over denominator 2 end fraction end style close parentheses over denominator 2 x cross times 2 cross times cos open parentheses begin display style fraction numerator 12 x plus 8 x over denominator 2 end fraction end style close parentheses cross times cos open parentheses begin display style fraction numerator 12 x minus 8 x over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 cross times sin open parentheses begin display style fraction numerator 12 x over denominator 2 end fraction end style close parentheses cross times cos open parentheses begin display style fraction numerator 4 x over denominator 2 end fraction end style close parentheses over denominator 2 x cross times 2 cross times cos open parentheses begin display style fraction numerator 20 x over denominator 2 end fraction end style close parentheses cross times cos open parentheses begin display style fraction numerator 4 x over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 cross times sin open parentheses begin display style 6 x end style close parentheses cross times cos open parentheses begin display style 2 x end style close parentheses over denominator 2 x cross times 2 cross times cos open parentheses begin display style 10 x end style close parentheses cross times cos open parentheses begin display style 2 x end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 cross times sin open parentheses begin display style 3 cross times 2 x end style close parentheses over denominator 2 cross times cos open parentheses begin display style 10 x end style close parentheses cross times 2 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 cross times 3 cross times sin open parentheses begin display style 2 x end style close parentheses over denominator 2 cross times cos open parentheses begin display style 10 x end style close parentheses cross times 2 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 cross times 3 over denominator 2 cross times cos open parentheses begin display style 10 x end style close parentheses end fraction end cell row blank equals cell fraction numerator 6 over denominator 2 cross times cos open parentheses begin display style 10 left parenthesis 0 right parenthesis end style close parentheses end fraction end cell row blank equals cell fraction numerator 6 over denominator 2 cross times cos open parentheses begin display style 0 end style close parentheses end fraction end cell row blank equals cell 6 over 2 end cell row blank equals 3 end table

Maka, nilai dari limit as x rightwards arrow 0 of fraction numerator sin open parentheses 8 x close parentheses plus sin open parentheses 4 x close parentheses over denominator 2 x left parenthesis cos open parentheses 12 x close parentheses plus cos open parentheses 8 x close parentheses right parenthesis end fraction adalah 3

Oleh karena itu, jawaban yang benar adalah E

0

Ruangguru

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved