Pertanyaan

x → 2 lim x 2 + 5 x + 6 x 2 − 10 x − 24 = ....

$x \to 2 lim \frac{x ^{2} - 10 x - 24}{x ^{2} + 5 x + 6}$ = ....

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style limit as straight x rightwards arrow 2 of fraction numerator straight x squared minus 10 straight x minus 24 over denominator straight x squared plus 5 straight x plus 6 end fraction equals negative 2 over 3 end style$

Pembahasan

soal di atas merupakan limit tak tentu fungsi aljabar yang penyelesaiannya menggunakan dalil L'hospital, yaitu dengan menggunakan turunan. Perhatikan perhitungan berikut ! Jadi,

soal di atas merupakan limit tak tentu fungsi aljabar yang penyelesaiannya menggunakan dalil L'hospital, yaitu dengan menggunakan turunan.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as straight x rightwards arrow straight a of fraction numerator straight f open parentheses straight x close parentheses over denominator straight g open parentheses straight x close parentheses end fraction end cell cell equals limit as straight x rightwards arrow straight a of end cell cell fraction numerator straight f apostrophe open parentheses straight x close parentheses over denominator straight g apostrophe open parentheses straight x close parentheses end fraction end cell end table end style$

Perhatikan perhitungan berikut !

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as straight x rightwards arrow 2 of fraction numerator straight x squared minus 10 straight x minus 24 over denominator straight x squared plus 5 straight x plus 6 end fraction end cell equals cell limit as straight x rightwards arrow 2 of fraction numerator 2 straight x minus 10 over denominator 2 straight x plus 5 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 2 close parentheses minus 10 over denominator 2 open parentheses 2 close parentheses plus 5 end fraction end cell row blank equals cell fraction numerator 4 minus 10 over denominator 4 plus 5 end fraction end cell row blank equals cell fraction numerator negative 6 over denominator 9 end fraction end cell row blank equals cell negative 6 over 9 end cell row blank equals cell negative 2 over 3 end cell end table end style$

Jadi, $begin mathsize 14px style limit as straight x rightwards arrow 2 of fraction numerator straight x squared minus 10 straight x minus 24 over denominator straight x squared plus 5 straight x plus 6 end fraction equals negative 2 over 3 end style$