RoboguruRoboguru
SD

Jikax→−3lim​x+3x2+4x+3​=a−1, nilai a adalah ...

Pertanyaan

Jikabegin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator x squared plus 4 x plus 3 over denominator x plus 3 end fraction equals a minus 1 end style, nilai begin mathsize 14px style a end style adalah ... 

P. Anggrayni

Master Teacher

Jawaban terverifikasi

Jawaban

 nilai begin mathsize 14px style a end style adalah negative 1.

Pembahasan

Jika menggunakan metode substitusi akan diperoleh nilai limit 0 over 0 seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 3 of fraction numerator x squared plus 4 x plus 3 over denominator x plus 3 end fraction end cell equals cell fraction numerator open parentheses negative 3 close parentheses squared plus 4 open parentheses negative 3 close parentheses plus 3 over denominator negative 3 plus 3 end fraction end cell row blank equals cell fraction numerator 9 minus 12 plus 3 over denominator negative 3 plus 3 end fraction end cell row blank equals cell 0 over 0 end cell end table

Oleh sebab itu gunakan metode pemfaktoran. Perhatikan perhitungan berikut ini

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 3 of fraction numerator x squared plus 4 x plus 3 over denominator x plus 3 end fraction end cell equals cell limit as x rightwards arrow negative 3 of fraction numerator open parentheses x plus 3 close parentheses open parentheses x plus 1 close parentheses over denominator open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow negative 3 of open parentheses x plus 1 close parentheses end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell negative 3 plus 1 end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell negative 2 end cell end table  

sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell a minus 1 end cell equals cell negative 2 end cell row a equals cell negative 2 plus 1 end cell row a equals cell negative 1 end cell end table  

Dengan demikian, nilai begin mathsize 14px style a end style adalah negative 1.

246

4.0 (7 rating)

Muhammad Ayatur Rahman

Mudah dimengerti

Pertanyaan serupa

Hitunglah nilai dari: x→1lim​1−x1​[1−x1−x20​−20].

37

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