Pertanyaan

Nilai

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

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

M. Alfi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

nilai adalah

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

Pembahasan

Untuk menyelesaikan limit tersebut, sederhanakan fungsi terlebehi dahulu Diperoleh Jadi, nilai adalah

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