Roboguru

Pertanyaan

Tentukan nilai limit dari:

f.

begin mathsize 14px style limit as p rightwards arrow negative 2 of fraction numerator begin display style 4 minus p squared end style over denominator 2 plus p end fraction end style

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as p rightwards arrow negative 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator begin display style 4 minus p squared end style over denominator 2 plus p end fraction end cell end table equals 4 end style.

Pembahasan

Jika kita menghitung nilai begin mathsize 14px style lim with italic p yields minus sign 2 below fraction numerator begin display style 4 minus sign italic p squared end style over denominator 2 plus italic p end fraction end style dengan cara substitusi langsung, maka kita akan memperoleh bentuk tak tentu begin mathsize 14px style 0 over 0 end style. Oleh karena itu, limit fungsi tersebut hendaknya diselesaikan dengan cara pemfaktoran, yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as p rightwards arrow negative 2 of fraction numerator begin display style 4 minus p squared end style over denominator 2 plus p end fraction end cell equals cell limit as p rightwards arrow negative 2 of fraction numerator up diagonal strike open parentheses 2 plus p close parentheses end strike to the power of 1 open parentheses 2 minus p close parentheses over denominator up diagonal strike 2 plus p end strike to the power of 1 end fraction end cell row blank equals cell limit as p rightwards arrow negative 2 of open parentheses 2 minus p close parentheses end cell row blank equals cell 2 minus open parentheses negative 2 close parentheses end cell row blank equals 4 end table end style

Dengan demikian, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as p rightwards arrow negative 2 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator begin display style 4 minus p squared end style over denominator 2 plus p end fraction end cell end table equals 4 end style.

13

5.0 (3 rating)

Pertanyaan serupa

Nilaidarix→2lim​x2−2xx2−x−2​adalah...

36

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 Ruangguru

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