Pertanyaan

Tentukan nilai limit tak hingga berikut! x → ∞ lim 4 x 2 + 3 x 2 x + 1

Tentukan nilai limit tak hingga berikut!

$x \to \infty lim \frac{2 x + 1}{4 x ^{2} + 3 x}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

.

$begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 2 x plus 1 over denominator 4 x squared plus 3 x end fraction equals 0 end style$ .

Pembahasan

Dengan mengalikan pembilang dan penyebut dengan , diperoleh Jadi .

$begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 2 x plus 1 over denominator 4 x squared plus 3 x end fraction end style$

Dengan mengalikan pembilang dan penyebut dengan , diperoleh

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

Jadi $begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 2 x plus 1 over denominator 4 x squared plus 3 x end fraction equals 0 end style$ .