Pertanyaan

x → 3 lim x 2 − x − 6 x 2 − 8 x + 15 = ....

$x \to 3 lim \frac{x ^{2} - 8 x + 15}{x ^{2} - x - 6}$ = ....

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style limit as straight x rightwards arrow 3 of fraction numerator straight x squared minus 8 straight x plus 15 over denominator straight x squared minus straight x minus 6 end fraction equals 5 over 8 end style$

Pembahasan

soal di atas merupakan limit tak tentu fungsi aljabar yang penyelesaiannya menggunakan faktorisasi. Perhatikan perhitungan berikut ! Jadi,

soal di atas merupakan limit tak tentu fungsi aljabar yang penyelesaiannya menggunakan faktorisasi. Perhatikan perhitungan berikut !

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as straight x rightwards arrow 3 of fraction numerator straight x squared minus 8 straight x plus 15 over denominator straight x squared minus straight x minus 6 end fraction end cell equals cell limit as straight x rightwards arrow 3 of fraction numerator up diagonal strike open parentheses straight x minus 3 close parentheses end strike open parentheses straight x plus 5 close parentheses over denominator up diagonal strike open parentheses straight x minus 3 close parentheses end strike open parentheses straight x plus 2 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 3 plus 5 close parentheses over denominator open parentheses 3 plus 2 close parentheses end fraction end cell row blank equals cell 8 over 5 end cell end table end style$

Jadi, $begin mathsize 14px style limit as straight x rightwards arrow 3 of fraction numerator straight x squared minus 8 straight x plus 15 over denominator straight x squared minus straight x minus 6 end fraction equals 5 over 8 end style$