Pertanyaan

x → ∞ lim 4 x − 2 x 2 − 5 x 3 3 x 3 − 2 x − 10 = …

$x \to \infty lim \frac{3 x ^{3} - 2 x - 10}{4 x - 2 x ^{2} - 5 x ^{3}} = \dots$

R. Subakti

Master Teacher

Mahasiswa/Alumni Universitas Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat: . Dengan demikian, nilai dari limit di atas adalah . Jadi, jawaban yang tepat adalah A.

Ingat: limit as x rightwards arrow infinity of k over x to the power of n equals k over infinity to the power of n equals 0 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 3 x cubed minus 2 x minus 10 over denominator 4 x minus 2 x squared minus 5 x cubed end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 3 x cubed minus 2 x minus 10 over denominator 4 x minus 2 x squared minus 5 x cubed end fraction times fraction numerator begin display style 1 over x cubed end style over denominator begin display style 1 over x cubed end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 3 x cubed over denominator x cubed end fraction end style minus begin display style fraction numerator 2 x over denominator x cubed end fraction end style minus begin display style 10 over x cubed end style over denominator begin display style fraction numerator 4 x over denominator x cubed end fraction end style minus begin display style fraction numerator 2 x squared over denominator x cubed end fraction end style minus begin display style fraction numerator 5 x cubed over denominator x cubed end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 3 minus 2 over x squared minus 10 over x cubed end style over denominator begin display style 4 over x squared minus 2 over x minus 5 end style end fraction end cell row blank equals cell fraction numerator begin display style 3 minus 2 over infinity squared minus 10 over infinity cubed end style over denominator begin display style 4 over infinity squared minus 2 over infinity minus 5 end style end fraction end cell row blank equals cell fraction numerator 3 minus 0 minus 0 over denominator 0 minus 0 minus 5 end fraction end cell row blank equals cell negative 3 over 5 end cell end table$

Dengan demikian, nilai dari limit di atas adalah size 14px minus size 14px 3 over size 14px 5 .

Jadi, jawaban yang tepat adalah A.