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Nilai

Pertanyaan

Nilai stack text lim end text with x rightwards arrow negative infinity below space open parentheses 2 x to the power of 4 minus 2 over x to the power of 5 close parentheses equals.... 

  1. negative infinity

  2. negative 100

  3. 5

  4. 10

  5. infinity

A. Azriah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Berikut langkah-langkah penyelesaian:

  1. Tentukan variabel berpangkat tertinggi pada fungsi polinomial.
  2. Faktorkan fungsi polinomial dengan mengeluarkan variabel berpangkat tertinggi.
  3. Gunakan sifat-sifat limit tak hingga untuk menentukan nilai limit fungsi polinomial tersebut.

Ingat: stack text lim end text with x rightwards arrow infinity below 1 over x to the power of n equals 0

Penyelesaian:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack text lim end text with x rightwards arrow negative infinity below open parentheses 2 x to the power of 4 minus 2 over x to the power of 5 close parentheses end cell equals cell stack text lim end text with x rightwards arrow negative infinity below open parentheses 2 x to the power of 4 minus 2 x to the power of negative 5 end exponent close parentheses space rightwards arrow text pangkat tertinggi end text space x to the power of 4 end cell row blank equals cell stack text lim end text with x rightwards arrow negative infinity below x to the power of 4 open parentheses 2 minus 2 x to the power of negative 9 end exponent close parentheses end cell row blank equals cell stack text lim end text with x rightwards arrow negative infinity below x to the power of 4 open parentheses 2 minus 2 over x to the power of 9 blank close parentheses end cell row blank equals cell stack text lim end text with x rightwards arrow negative infinity below x to the power of 4 times stack text lim end text with x rightwards arrow negative infinity below open parentheses 2 minus 2 over x to the power of 9 blank close parentheses blank end cell row blank equals cell limit as straight x rightwards arrow negative straight infinity of straight x to the power of 4 times open parentheses limit as straight x rightwards arrow negative straight infinity of 2 minus limit as straight x rightwards arrow negative straight infinity of open parentheses 2 over straight x to the power of 9 close parentheses blank close parentheses end cell row blank equals cell limit as straight x rightwards arrow negative straight infinity of straight x to the power of 4 times open parentheses limit as straight x rightwards arrow negative straight infinity of 2 minus 2 limit as straight x rightwards arrow negative straight infinity of open parentheses 1 over straight x to the power of 9 close parentheses blank close parentheses end cell row blank equals cell left parenthesis negative straight infinity right parenthesis to the power of 4 times open parentheses 2 minus 2 cross times 0 blank close parentheses end cell row blank equals cell straight infinity times 2 end cell row blank equals straight infinity end table end style

Oleh karena itu, jawaban yang benar adalah E.

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