Roboguru
SD

x→∞lim​(x+6x​​−x−2x​​)

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of x plus 6 square root of x end root minus square root of x minus 2 square root of x end root close parentheses end style  

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of x plus 6 square root of x end root minus square root of x minus 2 square root of x end root close parentheses end style adalah begin mathsize 14px style 4 end style.

Pembahasan

Menyelesaikan limit dengan mengalikan akar sekawan dan membagi semua suku dengan variabel yng memiliki pangkat tertinggi pada penyebut, dalam kasus ini begin mathsize 14px style square root of x end style, diperoleh

begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of x plus 6 square root of x end root minus square root of x minus 2 square root of x end root close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses square root of x plus 6 square root of x end root minus square root of x minus 2 square root of x end root close parentheses times fraction numerator square root of x plus 6 square root of x end root plus square root of x minus 2 square root of x end root over denominator square root of x plus 6 square root of x end root plus square root of x minus 2 square root of x end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x plus 6 square root of x minus x plus 2 square root of x over denominator square root of x plus 6 square root of x end root plus square root of x minus 2 square root of x end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 8 square root of x over denominator square root of x plus 6 square root of x end root plus square root of x minus 2 square root of x end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 8 square root of x over denominator square root of x end fraction end style over denominator begin display style fraction numerator square root of x plus 6 square root of x end root over denominator square root of x end fraction end style plus begin display style fraction numerator square root of x minus 2 square root of x end root over denominator square root of x end fraction end style end fraction end cell row blank equals cell fraction numerator 8 over denominator square root of begin display style fraction numerator x plus 6 square root of x over denominator x end fraction end style end root plus square root of fraction numerator x minus 2 square root of x over denominator x end fraction end root end fraction end cell row blank equals cell fraction numerator 8 over denominator square root of begin display style 1 plus 0 end style end root plus square root of 1 minus 0 end root end fraction end cell row blank equals cell fraction numerator 8 over denominator 1 plus 1 end fraction end cell row blank equals cell 8 over 2 end cell row blank equals 4 end table end style 

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of x plus 6 square root of x end root minus square root of x minus 2 square root of x end root close parentheses end style adalah begin mathsize 14px style 4 end style.

41

5.0 (1 rating)

Pertanyaan serupa

Nilai dari x→∞lim​(x2+x−1​−2x2+5x+1​)=....

121

4.2

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