Pertanyaan

x → ∞ lim ( x 2 − 3 x 4 + 2 x − 6 ) ( 5 x 4 + 8 x 3 − 12 x 2 − 14 x − 2 ) = ....

$x \to \infty lim \frac{( 5 x ^{4} + 8 x ^{3} - 12 x ^{2} - 14 x - 2 )}{( x ^{2} - 3 x ^{4} + 2 x - 6 )} = ....$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Dengan melakukan pembagian dengan variabel yang memiliki derajat tertinggi dan ingat bahwa , maka didapatkan: Jadi, jawaban yang tepat adalah E.

Dengan melakukan pembagian dengan variabel yang memiliki derajat tertinggi dan ingat bahwa limit as x rightwards arrow infinity of a over x to the power of n equals 0 , maka didapatkan:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator open parentheses 5 x to the power of 4 plus 8 x cubed minus 12 x squared minus 14 x minus 2 close parentheses over denominator open parentheses x squared minus 3 x to the power of 4 plus 2 x minus 6 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses begin display style fraction numerator 5 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 8 x cubed over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 12 x squared over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 14 x over denominator x to the power of 4 end fraction end style minus begin display style 2 over x to the power of 4 end style close parentheses over denominator open parentheses begin display style x squared over x to the power of 4 end style minus begin display style fraction numerator 3 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 2 x over denominator x to the power of 4 end fraction end style minus begin display style 6 over x to the power of 4 end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses begin display style 5 plus 8 over x minus 12 over x squared minus 14 over x cubed minus 2 over x to the power of 4 end style close parentheses over denominator open parentheses begin display style 1 over x squared minus 3 plus 2 over x cubed minus 6 over x to the power of 4 end style close parentheses end fraction end cell row blank equals cell fraction numerator 5 plus 0 minus 0 minus 0 minus 0 over denominator 0 minus 3 plus 0 minus 0 end fraction end cell row blank equals cell negative 5 over 3 end cell row blank equals cell negative 1 2 over 3 end cell end table$

Jadi, jawaban yang tepat adalah E.