Pertanyaan

x → ∞ lim x − 6 x 2 − 2 x 4 x 4 + 2 x 2 + 4 x = ...

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

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Menentukan limit fungsi suku banyak atau polinomdengan membagi pembilang dan penyebut pada fungsi dengan pangkat tertinggi. Ingat bahwa Pangkat tertinggi pada fungsi adalah , maka: Maka, nilai .

Menentukan limit fungsi suku banyak atau polinom dengan membagi pembilang dan penyebut pada fungsi dengan pangkat tertinggi.

Ingat bahwa

limit as x rightwards arrow infinity of c over x to the power of n equals 0

Pangkat tertinggi pada fungsi adalah , maka:

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

Maka, nilai $begin mathsize 14px style limit as x rightwards arrow infinity of space fraction numerator x to the power of 4 plus 2 x squared plus 4 x over denominator x minus 6 x squared minus 2 x to the power of 4 end fraction equals negative 1 half end style$ .