RoboguruRoboguru
SD

Hitunglah nilai dari x→0lim​x2+x​−2−x​​.

Pertanyaan

Hitunglah nilai dari begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of 2 plus x end root minus square root of 2 minus x end root over denominator x end fraction end style.

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

nilai dari limit tersebut adalah begin mathsize 14px style bottom enclose bold 1 over bold 2 square root of bold 2 end enclose end style.

Pembahasan

Menggunakan konsep penyelesaian limit dengan mengalikan sekawannya, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator square root of 2 plus x end root minus square root of 2 minus x end root over denominator x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator square root of 2 plus x end root minus square root of 2 minus x end root over denominator x end fraction times fraction numerator square root of 2 plus x end root plus square root of 2 minus x end root over denominator square root of 2 plus x end root plus square root of 2 minus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator left parenthesis 2 plus x right parenthesis minus left parenthesis 2 minus x right parenthesis over denominator x open parentheses square root of 2 plus x end root plus square root of 2 minus x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 x over denominator x open parentheses square root of 2 plus x end root plus square root of 2 minus x end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator 2 over denominator open parentheses square root of 2 plus x end root plus square root of 2 minus x end root close parentheses end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 2 plus square root of 2 end fraction end cell row blank equals cell fraction numerator 2 over denominator 2 square root of 2 end fraction equals fraction numerator 1 over denominator square root of 2 end fraction equals 1 half square root of 2 end cell end table end style 

Jadi, nilai dari limit tersebut adalah begin mathsize 14px style bottom enclose bold 1 over bold 2 square root of bold 2 end enclose end style.

60

5.0 (3 rating)

Pertanyaan serupa

Tentukan nilai limit dari fungsi-fungsi berikut ini: x→1lim​2−x2+3​1−x2​

12

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