Roboguru
SD

x→2lim​x+1−2x+5​3−2x+5​​=...

Pertanyaan

limit as x rightwards arrow 2 of fraction numerator 3 minus square root of 2 x plus 5 end root over denominator x plus 1 minus square root of 2 x plus 5 end root end fraction equals... 

  1. negative 2 

  2. negative 1 half 

  3. 0 

  4. 1 half 

  5. 2 

Y. Herlanda

Master Teacher

Mahasiswa/Alumni STKIP PGRI Jombang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah B.

Menentukan Nilai Limit Fungsi Aljabar dengan Aturan L'Hospital

Substitusikan nilai x equals 2 ke fungsi di bawah ini, sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator 3 minus square root of 2 x plus 5 end root over denominator x plus 1 minus square root of 2 x plus 5 end root end fraction end cell equals cell fraction numerator 3 minus square root of 2 open parentheses 2 close parentheses plus 5 end root over denominator 2 plus 1 minus square root of 2 open parentheses 2 close parentheses plus 5 end root end fraction end cell row blank equals cell fraction numerator 3 minus square root of 4 plus 5 end root over denominator 3 minus square root of 4 plus 5 end root end fraction end cell row blank equals cell fraction numerator 3 minus square root of 9 over denominator 3 minus square root of 9 end fraction end cell row blank equals cell fraction numerator 3 minus 3 over denominator 3 minus 3 end fraction end cell row blank equals cell 0 over 0 end cell end table 

Karena  0 over 0 merupakan bentuk tak tentu, maka bentuk tersebut dapat kita sederhanakan dengan menggunakan aturan L'Hospital sebagai berikut:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of fraction numerator 3 minus square root of 2 x plus 5 end root over denominator x plus 1 minus square root of 2 x plus 5 end root end fraction end cell equals cell limit as x rightwards arrow 2 of fraction numerator 3 minus open parentheses 2 x plus 5 close parentheses to the power of begin display style 1 half end style end exponent over denominator x plus 1 minus open parentheses 2 x plus 5 close parentheses to the power of 1 half end exponent end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator negative begin display style 1 half end style open parentheses 2 x plus 5 close parentheses to the power of negative 1 half end exponent cross times 2 over denominator 1 minus begin display style 1 half end style open parentheses 2 x plus 5 close parentheses to the power of negative 1 half end exponent cross times 2 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator negative begin display style fraction numerator 1 over denominator square root of 2 x plus 5 end root end fraction end style over denominator 1 minus begin display style fraction numerator 1 over denominator square root of 2 x plus 5 end root end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow 2 of fraction numerator negative begin display style fraction numerator 1 over denominator square root of 2 x plus 5 end root end fraction end style over denominator begin display style fraction numerator square root of 2 x plus 5 end root minus 1 over denominator square root of 2 x plus 5 end root end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow 2 of minus fraction numerator 1 over denominator up diagonal strike square root of 2 x plus 5 end root end strike end fraction cross times fraction numerator up diagonal strike square root of 2 x plus 5 end root end strike over denominator square root of 2 x plus 5 end root minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow 2 of minus fraction numerator 1 over denominator square root of 2 x plus 5 end root minus 1 end fraction end cell row blank equals cell negative fraction numerator 1 over denominator square root of 2 open parentheses 2 close parentheses plus 5 end root minus 1 end fraction end cell row blank equals cell negative fraction numerator 1 over denominator square root of 4 plus 5 end root minus 1 end fraction end cell row blank equals cell negative fraction numerator 1 over denominator square root of 9 minus 1 end fraction end cell row blank equals cell negative fraction numerator 1 over denominator 3 minus 1 end fraction end cell row blank equals cell negative 1 half end cell end table end style 

Dengan demikian, nilai dari limit as x rightwards arrow 2 of fraction numerator 3 minus square root of 2 x plus 5 end root over denominator x plus 1 minus square root of 2 x plus 5 end root end fraction equals negative 1 half.

Oleh karena itu, jawaban yang benar adalah B.

46

4.3 (3 rating)

Pertanyaan serupa

Hitunglah: a. x→3lim​x3−7x2+15x−9x3−8x2+21x−18​

41

5.0

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