Pertanyaan

Nilai x → 9 lim x − 3 x 2 − 7 x − 18 adalah ...

Nilai $x \to 9 lim \frac{x ^{2} - 7 x - 18}{x - 3}$ adalah ...

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai adalah 66.

nilai $begin mathsize 14px style limit as x rightwards arrow 9 of fraction numerator x squared minus 7 x minus 18 over denominator square root of x minus 3 end fraction end style$ adalah 66.

Pembahasan

disubtitusikan pada limit tersebut Karena menghasilkan limit tak tentu, maka nilai limit bisa ditentukan dengan metode pemfaktoran sebagai berikut. Jadi, nilai adalah 66.

disubtitusikan pada limit tersebut

$begin mathsize 14px style limit as x rightwards arrow 9 of fraction numerator x squared minus 7 x minus 18 over denominator square root of x minus 3 end fraction equals fraction numerator 9 squared minus 7 open parentheses 9 close parentheses minus 18 over denominator square root of 9 minus 3 end fraction equals 0 over 0 end style$

Karena menghasilkan limit tak tentu, maka nilai limit bisa ditentukan dengan metode pemfaktoran sebagai berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 9 of fraction numerator x squared minus 7 x minus 18 over denominator square root of x minus 3 end fraction end cell equals cell limit as x rightwards arrow 9 of fraction numerator open parentheses x minus 9 close parentheses open parentheses x plus 2 close parentheses over denominator square root of x minus 3 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space end cell equals cell limit as x rightwards arrow 9 of fraction numerator up diagonal strike open parentheses square root of x minus 3 close parentheses end strike open parentheses square root of x plus 3 close parentheses open parentheses x plus 2 close parentheses over denominator up diagonal strike open parentheses square root of x minus 3 close parentheses end strike end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space end cell equals cell open parentheses square root of 9 plus 3 close parentheses open parentheses 9 plus 2 close parentheses end cell row cell space space space space space space space space space space space space space space space space space space space space space space end cell equals cell open parentheses 3 plus 3 close parentheses 11 end cell row cell space space space space space space space space space space space space space space space space space space space space space space end cell equals 66 end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow 9 of fraction numerator x squared minus 7 x minus 18 over denominator square root of x minus 3 end fraction end style$ adalah 66.