Pertanyaan

Tentukan nilai limit berikut menggunakan cara pemfaktoran x → 3 lim x 2 − 7 x + 12 x 2 − x − 6

Tentukan nilai limit berikut menggunakan cara pemfaktoran

$x \to 3 lim \frac{x ^{2} - x - 6}{x ^{2} - 7 x + 12}$

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

.

$begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus x minus 6 over denominator x squared minus 7 x plus 12 end fraction equals negative 5 end style$ .

Pembahasan

Dengan terlebih dahulu melakukan pemfaktoran diperoleh Jadi .

$begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus x minus 6 over denominator x squared minus 7 x plus 12 end fraction end style$

Dengan terlebih dahulu melakukan pemfaktoran diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared minus x minus 6 over denominator x squared minus 7 x plus 12 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x minus 3 close parentheses open parentheses x plus 2 close parentheses over denominator open parentheses x minus 3 close parentheses open parentheses x minus 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x plus 2 close parentheses over denominator open parentheses x minus 4 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 3 close parentheses plus 2 over denominator open parentheses 3 close parentheses minus 4 end fraction end cell row blank equals cell fraction numerator 5 over denominator negative 1 end fraction end cell row blank equals cell negative 5 end cell end table end style$

Jadi $begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus x minus 6 over denominator x squared minus 7 x plus 12 end fraction equals negative 5 end style$ .