Tentukan nilai limit fungsi berikut x→3limx2−9x3−27

Pertanyaan

Tentukan nilai limit fungsi berikut

$begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x cubed minus 27 over denominator x squared minus 9 end fraction end style$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

nilai limit dari $begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x cubed minus 27 over denominator x squared minus 9 end fraction end style$ adalah

Pembahasan

Untuk menyelesaikan permasalahan soal limit seperti ini, langkah pertamanya adalah dengan memfaktorkan bentuk pembilang dan penyebutnya agar bisa disederhanakan, maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x cubed minus 27 over denominator x squared minus 9 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator up diagonal strike left parenthesis x minus 3 right parenthesis end strike left parenthesis x squared plus 3 x plus 9 right parenthesis over denominator up diagonal strike left parenthesis x minus 3 right parenthesis end strike left parenthesis x plus 3 right parenthesis end fraction end cell row blank equals cell fraction numerator 3 squared plus 3 left parenthesis 3 right parenthesis plus 9 over denominator 3 plus 3 end fraction end cell row blank equals cell fraction numerator 9 plus 9 plus 9 over denominator 6 end fraction end cell row blank equals cell 27 over 6 end cell row blank equals cell 9 over 2 end cell end table end style$

Jadi, nilai limit dari $begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x cubed minus 27 over denominator x squared minus 9 end fraction end style$ adalah