x→∞lim 2x9−14x7−8x3+3x=....

Pertanyaan

$limit as x rightwards arrow infinity of space fraction numerator 4 x to the power of 7 minus 8 x cubed plus 3 x over denominator 2 x to the power of 9 minus 1 end fraction equals...$ .

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Bagi setiap suku dengan variabel pangkat tertinggi pada penyebut, sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator 4 x to the power of 7 minus 8 x cubed plus 3 x over denominator 2 x to the power of 9 minus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 4 x to the power of 7 over denominator x to the power of 9 end fraction end style minus begin display style fraction numerator 8 x cubed over denominator x to the power of 9 end fraction end style plus begin display style fraction numerator 3 x over denominator x to the power of 9 end fraction end style over denominator begin display style fraction numerator 2 x to the power of 9 over denominator x to the power of 9 end fraction end style minus begin display style 1 over x to the power of 9 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style 4 over x squared minus 8 over x to the power of 6 plus 3 over x to the power of 8 end style over denominator begin display style 2 minus 1 over x to the power of 9 end style end fraction end cell end table$

ingat bahwa limit as x rightwards arrow infinity of a over x to the power of n equals 0 maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator begin display style 4 over x squared minus 8 over x to the power of 6 plus 3 over x to the power of 8 end style over denominator begin display style 2 minus 1 over x to the power of 9 end style end fraction end cell equals cell fraction numerator 0 minus 0 plus 0 over denominator 2 minus 0 end fraction end cell row blank equals cell 0 over 2 end cell row blank equals 0 row blank blank blank end table$

Jadi, jawaban yang tepat adalah D.