Pertanyaan

Nilai x → ∞ lim 6 x 4 + 7 x 3 − 8 3 x 4 − 5 x 2 + 4 adalah ....

Nilai $x \to \infty lim \frac{3 x ^{4} - 5 x ^{2} + 4}{6 x ^{4} + 7 x ^{3} - 8}$ adalah $....$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai .

nilai $begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 3 x to the power of 4 minus 5 x squared plus 4 over denominator 6 x to the power of 4 plus 7 x cubed minus 8 end fraction equals 1 half end style$ .

Pembahasan

Rumus dasar limit tak hingga dengan adalah bilangan real dan adalah bilangan asli. Sehingga kita bagi pembilang dan penyebutnya dengan . Jadi, nilai .

Rumus dasar limit tak hingga dengan adalah bilangan real dan adalah bilangan asli. Sehingga kita bagi pembilang dan penyebutnya dengan .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 3 x to the power of 4 minus 5 x squared plus 4 over denominator 6 x to the power of 4 plus 7 x cubed minus 8 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 3 x to the power of 4 over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 5 x squared over denominator x to the power of 4 end fraction end style plus begin display style 4 over x to the power of 4 end style over denominator begin display style fraction numerator 6 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 7 x cubed over denominator x to the power of 4 end fraction end style minus begin display style 8 over x to the power of 4 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 3 minus begin display style 5 over x squared end style plus begin display style 4 over x to the power of 4 end style over denominator 6 plus begin display style 7 over x end style minus begin display style 8 over x to the power of 4 end style end fraction end cell row blank equals cell fraction numerator 3 minus 0 plus 0 over denominator 6 plus 0 minus 0 end fraction end cell row blank equals cell 3 over 6 end cell row blank equals cell 1 half end cell end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 3 x to the power of 4 minus 5 x squared plus 4 over denominator 6 x to the power of 4 plus 7 x cubed minus 8 end fraction equals 1 half end style$ .