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Hasil dari x→∞lim​8−x34x3 −x2−x+5​=....

Pertanyaan

Hasil dari limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 3 space end exponent minus x squared minus x plus 5 over denominator 8 minus x cubed end fraction equals....

  1. negative 4

  2. negative 1 half

  3. 0

  4. 1 half

     

  5. 4

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah A.

Soal limit di atas merupakan limit tak hingga. Jika diselesaikan dengan menggunakan metode substitusi, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 3 space end exponent minus x squared minus x plus 5 over denominator 8 minus x cubed end fraction end cell equals cell fraction numerator infinity minus infinity minus infinity plus 5 over denominator 8 minus infinity end fraction end cell row blank equals cell fraction numerator infinity minus infinity over denominator negative infinity end fraction end cell end table

Karena infinity minus infinity tidak tentu, maka soal tersebut perlu diselesaikan dengan cara lain.

Ingat bahwa pada limit tak hingga, berlaku:

limit as x rightwards arrow infinity of 1 over x equals 0  limit as x rightwards arrow infinity of c over x to the power of n equals 0

Diperoleh,

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 3 space end exponent minus x squared minus x plus 5 over denominator 8 minus x cubed end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 3 space end exponent minus x squared minus x plus 5 over denominator 8 minus 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 4 minus begin display style 1 over x end style minus begin display style 1 over x squared end style plus begin display style 5 over x cubed end style over denominator begin display style 8 over x cubed end style minus 1 end fraction end cell row blank equals cell fraction numerator 4 minus limit as x rightwards arrow infinity of begin display style 1 over x end style minus limit as x rightwards arrow infinity of begin display style 1 over x squared end style plus limit as x rightwards arrow infinity of begin display style 5 over x cubed end style over denominator limit as x rightwards arrow infinity of begin display style 8 over x cubed end style minus 1 end fraction end cell row blank equals cell fraction numerator 4 minus 0 minus 0 plus 0 over denominator 0 minus 1 end fraction end cell row blank equals cell negative 4 end cell end table

Dengan demikian, hasil dari limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 3 space end exponent minus x squared minus x plus 5 over denominator 8 minus x cubed end fraction equals negative 4.

Oleh karena itu, jawaban yang benar adalah A.

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