Roboguru
SD

x→∞lim​ (x+2−x2−2x+6​)=.....

Pertanyaan

limit as x rightwards arrow infinity of space open parentheses x plus 2 minus square root of x squared minus 2 x plus 6 end root close parentheses equals.....

  1. negative infinity

  2. 0

  3. 2

  4. 3

  5. infinity

T. Prita

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Nilai limit tak hingga dari suatu fungsi bentuk akar dapat ditentukan sebagai berikut.

begin mathsize 12px style limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root close parentheses equals open curly brackets table row cell infinity comma space text untuk end text space a greater than p end cell row cell table attributes columnalign left end attributes row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space text untuk end text space a equals p end cell row cell negative infinity comma space text untuk end text space a less than p end cell end table end cell end table close end style

Diketahui: 

limit as x rightwards arrow infinity of space open parentheses x plus 2 minus square root of x squared minus 2 x plus 6 end root close parentheses, dapat ditulis:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space open parentheses x plus 2 minus square root of x squared minus 2 x plus 6 end root close parentheses end cell equals cell limit as x rightwards arrow infinity of space open parentheses square root of open parentheses x plus 2 close parentheses squared end root minus square root of x squared minus 2 x plus 6 end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of space open parentheses square root of x squared plus 4 x plus 4 end root minus square root of x squared minus 2 x plus 6 end root close parentheses end cell end table end style

Bentuk soal limit di atas memiliki nilai a equals p equals 1, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space open parentheses square root of x squared plus 4 x plus 4 end root minus square root of x squared minus 2 x plus 6 end root close parentheses end cell equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator 4 minus open parentheses negative 2 close parentheses over denominator 2 square root of 1 end fraction end cell row blank equals cell 6 over 2 end cell row blank equals 3 end table

Oleh karena itu, jawaban yang benar adalah D.

142

4.8 (11 rating)

Pertanyaan serupa

Nilai dari ekspresi x→∞lim​x2−2x+5​−x2+2x+10​ adalah...

142

4.3

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