Roboguru

Nilai

Pertanyaan

Nilai begin mathsize 14px style limit as x rightwards arrow 2 of open parentheses fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 over denominator x minus 2 end fraction close parentheses equals horizontal ellipsis. end style   space 

Pembahasan Soal:

Untuk menyelesaikan limit tersebut, sederhanakan fungsi terlebehi dahulu

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 over denominator x minus 2 end fraction end cell equals cell fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 open parentheses x plus 1 close parentheses over denominator x squared minus x minus 2 end fraction end cell row blank equals cell fraction numerator 6 minus 2 open parentheses x plus 1 close parentheses over denominator x squared minus x minus 2 end fraction end cell row blank equals cell fraction numerator 6 minus 2 x minus 2 over denominator x squared minus x minus 2 end fraction end cell row blank equals cell fraction numerator negative 2 x plus 4 over denominator x squared minus x minus 2 end fraction end cell row blank equals cell fraction numerator negative 2 left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis end fraction end cell row blank equals cell negative fraction numerator 2 over denominator x plus 1 end fraction end cell end table end style  

Diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of open parentheses fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 over denominator x minus 2 end fraction close parentheses end cell equals cell limit as x rightwards arrow 2 of fraction numerator negative 2 over denominator left parenthesis x plus 1 right parenthesis end fraction end cell row blank equals cell fraction numerator negative 2 over denominator open parentheses 2 plus 1 close parentheses end fraction equals negative 2 over 3 end cell row blank blank blank end table end style  

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 2 of open parentheses fraction numerator 6 over denominator x squared minus x minus 2 end fraction minus fraction numerator 2 over denominator x minus 2 end fraction close parentheses end style adalah begin mathsize 14px style negative 2 over 3 end style    undefined 

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