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x→∞lim​4x−2x2−5x33x3−2x−10​=…

Pertanyaan

begin mathsize 14px style 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 equals horizontal ellipsis end style 

  1. begin mathsize 14px style negative 3 over 5 end style 

  2. begin mathsize 14px style negative 3 over 4 end style 

  3. begin mathsize 14px style 0 end style 

  4. size 14px 3 over size 14px 5 

  5. size 14px 3 over size 14px 4 

R. Subakti

Master Teacher

Mahasiswa/Alumni Universitas Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

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.

157

5.0 (4 rating)

Nasya Relyta Andrianty

Ini yang aku cari!

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