Pertanyaan

Nilai x → − 3 lim 5 x + 15 2 x 2 + 6 x adalah ...

Nilai $x \to - 3 lim \frac{2 x ^{2} + 6 x}{5 x + 15}$ adalah ...

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction end style$ adalah

Pembahasan

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

disubtitusikan pada limit tersebut

$begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction equals limit as x rightwards arrow negative 3 of fraction numerator 2 left parenthesis negative 3 right parenthesis squared plus 6 left parenthesis negative 3 right parenthesis over denominator 5 left parenthesis negative 3 right parenthesis plus 15 end fraction equals 0 over 0 end style$

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

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction end cell equals cell limit as x rightwards arrow negative 3 of fraction numerator 2 x up diagonal strike left parenthesis x plus 3 right parenthesis end strike over denominator 5 up diagonal strike left parenthesis x plus 3 right parenthesis end strike end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell fraction numerator 2 left parenthesis negative 3 right parenthesis over denominator 5 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell fraction numerator negative 6 over denominator 5 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell negative 1 1 fifth end cell end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow negative 3 of fraction numerator 2 x squared plus 6 x over denominator 5 x plus 15 end fraction end style$ adalah .