Pertanyaan

Tentukan nilai x → ∞ lim 3 x 4 − 7 x 5 − 3 x 2 + 6 6 x 3 − 5 x 5 − 4 x 4 + 2 x 2 .

Tentukan nilai $x \to \infty lim \frac{6 x ^{3} - 5 x ^{5} - 4 x ^{4} + 2 x ^{2}}{3 x ^{4} - 7 x ^{5} - 3 x ^{2} + 6}$ .

A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

nilai limit tersebut adalah .

nilai limit tersebut adalah 5 over 7

Pembahasan

Limit fungsi aljabar di atas dapat diselesaikan dengan membagi setiap variabeldengan variabel pangkat terbesar sebagai berikut: Dengan demikian, nilai limit tersebut adalah .

Limit fungsi aljabar di atas dapat diselesaikan dengan membagi setiap variabel dengan variabel pangkat terbesar sebagai berikut:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 6 x cubed minus 5 x to the power of 5 minus 4 x to the power of 4 plus 2 x squared over denominator 3 x to the power of 4 minus 7 x to the power of 5 minus 3 x squared plus 6 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses begin display style fraction numerator 6 x cubed over denominator x to the power of 5 end fraction end style minus begin display style fraction numerator 5 x to the power of 5 over denominator x to the power of 5 end fraction end style minus begin display style fraction numerator 4 x to the power of 4 over denominator x to the power of 5 end fraction end style plus begin display style fraction numerator 2 x squared over denominator x to the power of 5 end fraction end style close parentheses over denominator open parentheses begin display style fraction numerator 3 x to the power of 4 over denominator x to the power of 5 end fraction end style minus begin display style fraction numerator 7 x to the power of 5 over denominator x to the power of 5 end fraction end style minus begin display style fraction numerator 3 x squared over denominator x to the power of 5 end fraction end style plus begin display style 6 over x to the power of 5 end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses begin display style 6 over x squared minus 5 minus 4 over x plus 2 over x cubed end style close parentheses over denominator open parentheses begin display style 3 over x minus 7 minus 3 over x cubed plus 6 over x to the power of 5 end style close parentheses end fraction end cell row blank equals cell fraction numerator negative 5 over denominator negative 7 end fraction end cell row blank equals cell 5 over 7 end cell end table end style$

Dengan demikian, nilai limit tersebut adalah 5 over 7 .