Pertanyaan

Tentukan nilai limit tak hingga berikut! x → ∞ lim 3 x 2 + x 4 x 3 − 2 x

Tentukan nilai limit tak hingga berikut!

$x \to \infty lim \frac{4 x ^{3} - 2 x}{3 x ^{2} + x}$

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

$begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 4 x cubed minus 2 x over denominator 3 x squared plus x end fraction equals infinity end style$ .

Pembahasan

Dengan mengalikan pembilang dan penyebut dengan , diperoleh Jadi .

$begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 4 x cubed minus 2 x over denominator 3 x squared plus x end fraction end style$

Dengan mengalikan pembilang dan penyebut dengan , diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 4 x cubed minus 2 x over denominator 3 x squared plus x end fraction end cell equals cell limit as x rightwards arrow infinity of open parentheses fraction numerator 4 x cubed minus 2 x over denominator 3 x squared plus x end fraction close parentheses times fraction numerator open parentheses begin display style 1 over x cubed end style close parentheses over denominator open parentheses begin display style 1 over x cubed end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 4 minus begin display style 2 over x squared end style over denominator begin display style 3 over x end style plus begin display style 1 over x squared end style end fraction end cell row blank equals cell fraction numerator 4 minus 0 over denominator begin display style 0 plus 0 end style end fraction end cell row blank equals cell 4 over 0 end cell row blank equals infinity end table end style$

Jadi $begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 4 x cubed minus 2 x over denominator 3 x squared plus x end fraction equals infinity end style$ .