x→−2lim​x3+8x3+x2+2x+8​=....

Pertanyaan

limit as x rightwards arrow negative 2 of fraction numerator x cubed plus x squared plus 2 x plus 8 over denominator x cubed plus 8 end fraction equals.... 

  1. size 14px 5 over size 14px 6 

  2. size 14px 2 over size 14px 3 

  3. size 14px 1 over size 14px 2 

  4. size 14px 1 over size 14px 3 

  5. size 14px 1 over size 14px 6 

E. Safitri

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Pembahasan
  • Subtitusi nilai x equals negative 2

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of fraction numerator x cubed plus x squared plus 2 x plus 8 over denominator x cubed plus 8 end fraction end cell equals cell fraction numerator open parentheses negative 2 close parentheses cubed plus open parentheses negative 2 close parentheses squared plus 2 open parentheses negative 2 close parentheses plus 8 over denominator open parentheses negative 2 close parentheses cubed plus 8 end fraction end cell row blank equals cell fraction numerator negative 8 plus 4 minus 4 plus 8 over denominator negative 8 plus 8 end fraction end cell row blank equals cell fraction numerator negative 12 plus 12 over denominator negative 8 plus 8 end fraction end cell row blank equals cell 0 over 0 end cell end table

Karena 0 over 0 tak tentu, maka nilai limit tersebut dapat dihitung dengan menggunakan metode pemfaktoran : 

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of fraction numerator x cubed plus x squared plus 2 x plus 8 over denominator x cubed plus 8 end fraction end cell equals cell limit as x rightwards arrow negative 2 of fraction numerator open parentheses x plus 2 close parentheses open parentheses x squared minus x plus 4 close parentheses over denominator open parentheses x plus 2 close parentheses open parentheses x squared minus 2 x plus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator up diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x squared minus x plus 4 close parentheses over denominator up diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x squared minus 2 x plus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator open parentheses x squared minus x plus 4 close parentheses over denominator open parentheses x squared minus 2 x plus 4 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses open parentheses negative 2 close parentheses squared minus open parentheses negative 2 close parentheses plus 4 close parentheses over denominator open parentheses open parentheses negative 2 close parentheses squared minus 2 open parentheses negative 2 close parentheses plus 4 close parentheses end fraction end cell row blank equals cell fraction numerator 4 plus 2 plus 4 over denominator 4 plus 4 plus 4 end fraction end cell row blank equals cell 10 over 12 end cell row blank equals cell 5 over 6 end cell end table

Jadi, limit as x rightwards arrow negative 2 of fraction numerator x cubed plus x squared plus 2 x plus 8 over denominator x cubed plus 8 end fraction equals 5 over 6.


Oleh karena itu, jawaban yang tepat adalah A.

59

5.0 (3 rating)

Pertanyaan serupa

x→1lim​1−x2x2+3​−x−1​=...

203

4.9

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

Fitur Roboguru

Topik Roboguru

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