Tentukan nilai limit fungsi berikut ini: c) x→3limx2−x−6x2−9

Pertanyaan

Tentukan nilai limit fungsi berikut ini:

c) $begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator x squared minus x minus 6 end fraction end style$

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator x squared minus x minus 6 end fraction equals 6 over 5 end style$

Pembahasan

Dengan menggunakan metode pemfaktoran.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator x squared minus x minus 6 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x plus 3 close parentheses up diagonal strike open parentheses x minus 3 close parentheses end strike over denominator open parentheses x plus 2 close parentheses up diagonal strike open parentheses x minus 3 close parentheses end strike end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator x plus 3 over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 3 plus 3 over denominator 3 plus 2 end fraction end cell row blank equals cell 6 over 5 end cell end table end style$

Jadi, $begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator x squared minus x minus 6 end fraction equals 6 over 5 end style$