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Nilaix→3lim​(x2−2x−316​−x−34​) adalah ...

Pertanyaan

Nilaibegin mathsize 14px style limit as x rightwards arrow 3 of open parentheses fraction numerator 16 over denominator x squared minus 2 x minus 3 end fraction minus fraction numerator 4 over denominator x minus 3 end fraction close parentheses end style adalah ...

  1. begin mathsize 14px style negative 4 end style 

  2. begin mathsize 14px style negative 1 end style 

  3. begin mathsize 14px style negative 1 third end style  

  4. undefined 

  5. begin mathsize 14px style 1 end style 

S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Untuk mencari nilai limit, kita coba substitusikan dahulu x equals 3 ke persamaaan:

limit as x rightwards arrow 3 of open parentheses fraction numerator 16 over denominator x squared minus 2 x minus 3 end fraction minus fraction numerator 4 over denominator x minus 3 end fraction close parentheses equals fraction numerator 16 over denominator left parenthesis 3 right parenthesis squared minus 2 left parenthesis 3 right parenthesis minus 3 end fraction minus fraction numerator 4 over denominator left parenthesis 3 right parenthesis minus 3 end fraction

Setelah disubstitusikan, ternyata menghasilkan penyebut 0 sehingga kita faktorkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of open parentheses fraction numerator 16 over denominator x squared minus 2 x minus 3 end fraction minus fraction numerator 4 over denominator x minus 3 end fraction close parentheses end cell equals cell limit as x rightwards arrow 3 of open parentheses fraction numerator 16 minus 4 left parenthesis x plus 1 right parenthesis over denominator x squared minus 2 x minus 3 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 3 of open parentheses fraction numerator 16 minus 4 x minus 4 over denominator x squared minus 2 x minus 3 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 3 of open parentheses fraction numerator 12 minus 4 x over denominator x squared minus 2 x minus 3 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 3 of open parentheses fraction numerator negative 4 up diagonal strike left parenthesis x minus 3 right parenthesis end strike over denominator up diagonal strike left parenthesis x minus 3 right parenthesis end strike left parenthesis x plus 1 right parenthesis end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 3 of open parentheses fraction numerator negative 4 over denominator left parenthesis x plus 1 right parenthesis end fraction close parentheses end cell row blank equals cell fraction numerator negative 4 over denominator 3 plus 1 end fraction end cell row blank equals cell negative 1 end cell end table

Oleh karena itu, jawaban yang tepat adalah B.

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