Pertanyaan

x → ∞ lim 2 x 4 + x − 1 6 x 5 − 7 x 2 + 1 = ... .

$x \to \infty lim \frac{6 x ^{5} - 7 x ^{2} + 1}{2 x ^{4} + x - 1} = ...$ .

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Bagi setiap suku dengan variabel pangkat tertinggi pada penyebut Ingat bahwa sehingga Jadi, jawaban yang tepat adalah E.

Bagi setiap suku dengan variabel pangkat tertinggi pada penyebut

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator 6 x to the power of 5 minus 7 x squared plus 1 over denominator 2 x to the power of 4 plus x minus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 6 x to the power of 5 over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 7 x squared over denominator x to the power of 4 end fraction end style plus begin display style 1 over x to the power of 4 end style over denominator begin display style fraction numerator 2 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style x over x to the power of 4 end style minus begin display style 1 over x to the power of 4 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style 6 x minus 7 over x squared plus 1 over x to the power of 4 end style over denominator begin display style 2 plus 1 over x cubed minus 1 over x to the power of 4 end style end fraction end cell row blank blank blank end table$

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

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

Jadi, jawaban yang tepat adalah E.