Ingat! Diketahui . Misalkan: Maka, Sehingga, . Jadi, jawaban yang tepat adalah D.

Nilai

Pertanyaan

Nilai $limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 over x end style over denominator tan space begin display style 2 over x end style end fraction equals...$ $begin mathsize 14px style space end style$

4 $space$
24 $space$
16 $space$
12 $space$

Pembahasan Soal:

Ingat!

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin space begin display style a x end style over denominator tan space b x end fraction end cell equals cell a over b end cell row cell limit as x rightwards arrow 0 of fraction numerator k times sin space begin display style x end style over denominator tan space x end fraction end cell equals cell k times limit as x rightwards arrow 0 of fraction numerator sin space begin display style x end style over denominator tan space x end fraction equals k times 1 equals k end cell end table$

Diketahui $limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 over x end style over denominator tan space begin display style 2 over x end style end fraction$ .

$limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 over x end style over denominator tan space begin display style 2 over x end style end fraction equals limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 1 over x end style over denominator tan space begin display style 2 1 over x end style end fraction$

Misalkan:

$a equals 1 over x comma space maka space x equals 1 over a x rightwards arrow infinity comma space maka space a rightwards arrow 0$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 8 space sin space begin display style 3 1 over x end style over denominator tan space begin display style 2 1 over x end style end fraction end cell equals cell limit as a rightwards arrow 0 of fraction numerator 8 space sin space begin display style 3 a end style over denominator tan space begin display style 2 a end style end fraction end cell row blank equals cell 8 times 3 over 2 end cell row blank equals 12 end table$

Sehingga, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 8 space sin space begin display style 3 1 over x end style over denominator tan space begin display style 2 1 over x end style end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 12 end table$ .

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Juni 2021

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Download di Google Play

Download di Appstore

Download di App Gallery

Produk Ruangguru

Produk Lainnya

Bantuan & Panduan

Hubungi Kami

081578200000

[email protected]

02140008000

Ikuti Kami

Instagram

Facebook

Twitter

Youtube