Roboguru

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 4 of open parentheses fraction numerator 4 minus x over denominator 5 minus square root of x squared plus 9 end root end fraction close parentheses end style

  1. begin mathsize 14px style 2 end style

  2. begin mathsize 14px style 5 over 3 end style

  3. begin mathsize 14px style 10 over 7 end style

  4. begin mathsize 14px style 5 over 4 end style

  5. begin mathsize 14px style 10 over 9 end style

Pembahasan Soal:

Untuk menyelesaikan bentuk limit diatas kita dapat menggunkan metode mengalikan akar sekawan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of fraction numerator 4 minus x over denominator 5 minus square root of x squared plus 9 end root end fraction end cell equals cell limit as x rightwards arrow 4 of fraction numerator 4 minus x over denominator 5 minus square root of x squared plus 9 end root end fraction cross times fraction numerator 5 plus square root of x squared plus 9 end root over denominator 5 plus square root of x squared plus 9 end root end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator open parentheses 4 minus x close parentheses open parentheses 5 plus square root of x squared plus 9 end root close parentheses over denominator 25 minus open parentheses x squared plus 9 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator left parenthesis 4 minus x right parenthesis open parentheses 5 plus square root of x squared plus 9 end root close parentheses over denominator negative x squared plus 16 end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator left parenthesis 4 minus x right parenthesis open parentheses 5 plus square root of x squared plus 9 end root close parentheses over denominator open parentheses 4 minus x close parentheses open parentheses 4 plus x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator blank over denominator open parentheses 4 plus x close parentheses end fraction end cell row blank equals cell fraction numerator 5 plus square root of 4 squared plus 9 end root over denominator 4 plus 4 end fraction end cell row blank equals cell fraction numerator 5 plus 5 over denominator 8 end fraction end cell row blank equals cell 10 over 8 end cell row blank equals cell 5 over 4 end cell end table end style

 

Jadi, jawaban yang tepat adalah D

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved