x→0lim​1+x​−1−x​x​=....

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x over denominator square root of 1 plus x end root minus square root of 1 minus x end root end fraction equals end style....

S. Dwi

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari limit as x rightwards arrow 0 of fraction numerator x over denominator square root of 1 plus x end root minus square root of 1 minus x end root end fraction equals 1.

Pembahasan

Perhatikan bahwa:

Saat dilakukan substitusi, limit di atas akan bernilai

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator x over denominator square root of 1 plus x end root minus square root of 1 minus x end root end fraction end cell equals cell fraction numerator 0 over denominator square root of 1 plus 0 end root minus square root of 1 minus 0 end root end fraction end cell row blank equals cell fraction numerator 0 over denominator square root of 1 minus square root of 1 end fraction end cell row blank equals cell 0 over 0 end cell end table

Karena hasilnya masih dalam bentuk 0 over 0, maka selesaikan dengan metode mengalikan akar sekawan.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of fraction numerator x over denominator square root of 1 plus x end root minus square root of 1 minus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x over denominator square root of 1 plus x end root minus square root of 1 minus x end root end fraction cross times fraction numerator square root of 1 plus x end root plus square root of 1 minus x end root over denominator square root of 1 plus x end root plus square root of 1 minus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x open parentheses square root of 1 plus x end root plus square root of 1 minus x end root close parentheses over denominator open parentheses square root of 1 plus x end root close parentheses squared minus open parentheses square root of 1 minus x end root close parentheses squared end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x open parentheses square root of 1 plus x end root plus square root of 1 minus x end root close parentheses over denominator 1 plus x minus left parenthesis 1 minus x right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator x open parentheses square root of 1 plus x end root plus square root of 1 minus x end root close parentheses over denominator 1 plus x minus 1 plus x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x open parentheses square root of 1 plus x end root plus square root of 1 minus x end root close parentheses over denominator 2 up diagonal strike x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator square root of 1 plus x end root plus square root of 1 minus x end root over denominator 2 end fraction end cell row blank equals cell fraction numerator square root of 1 plus 0 end root plus square root of 1 minus 0 end root over denominator 2 end fraction end cell row blank equals cell fraction numerator square root of 1 plus square root of 1 over denominator 2 end fraction end cell row blank equals cell fraction numerator 1 plus 1 over denominator 2 end fraction end cell row blank equals cell 2 over 2 end cell row blank equals 1 end table

Dengan demikian, nilai dari limit as x rightwards arrow 0 of fraction numerator x over denominator square root of 1 plus x end root minus square root of 1 minus x end root end fraction equals 1.

303

4.8 (24 rating)

Alyaa Hafizhah Aurora Stya Lacksana

Pembahasan lengkap banget

Pertanyaan serupa

x→64lim​x31​−4x−64​= ...

23

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