Pertanyaan

x → ∞ lim 2 x 4 + 3 4 x 3 + x 2 + 1 = ...

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

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

diperoleh .

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

Pembahasan

Gunakan konsep limit tak hingga. Perhatikan perhitungan berikut. Jadi, diperoleh .

Gunakan konsep limit tak hingga.

Perhatikan perhitungan berikut.

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

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