Nilai X→∞lim 2x−31−5x= ....

Pertanyaan

Nilai $stack text lim end text with X rightwards arrow infinity below space fraction numerator 1 minus 5 x over denominator 2 x minus 3 end fraction equals space....$

$-\infty$
$-\frac52$
$\frac12$
$\frac53$
$\infty$

A. Azriah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Berikut langkah-langkah penyelesaian:

Tentukan variabel berpangkat tertinggi pada penyebut fungsi rasional.
Bagilah pembilang dan penyebut pada fungsi rasional dengan variabel berpangkat tertinggi.
Gunakan sifat-sifat limit tak hingga untuk menentukan nilai limit fungsi rasional tersebut.

Ingat: $\underset{x\rightarrow\infty}{\text{lim}}\frac1{x^n}=0\quad$

Penyelesaian:

$table attributes columnalign right center left columnspacing 0px end attributes row cell stack text lim end text with x rightwards arrow infinity below fraction numerator 1 minus 5 x over denominator 2 x minus 3 end fraction end cell equals cell stack text lim end text with x rightwards arrow infinity below fraction numerator 1 over x minus fraction numerator 5 x over denominator x end fraction over denominator fraction numerator 2 x over denominator x end fraction minus 3 over x end fraction end cell row blank equals cell stack text lim end text with x rightwards arrow infinity below fraction numerator 1 over x minus 5 over denominator 2 minus 3 over x end fraction end cell row blank equals cell fraction numerator stack text lim end text with x rightwards arrow infinity below 1 over x minus stack text lim end text with x rightwards arrow infinity below 5 over denominator stack text lim end text with x rightwards arrow infinity below 2 minus stack text lim end text with x rightwards arrow infinity below 3 over x end fraction end cell row blank equals cell fraction numerator stack text lim end text with x rightwards arrow infinity below 1 over x minus stack text lim end text with x rightwards arrow infinity below 5 over denominator stack text lim end text with x rightwards arrow infinity below 2 minus 3 stack text lim end text with x rightwards arrow infinity below 1 over x end fraction end cell row blank equals cell fraction numerator 0 minus 5 over denominator 2 minus 0 end fraction end cell row blank equals cell negative 5 over 2 end cell end table$

Oleh karena itu, jawaban yang benar adalah B.