x→∞lim​ (x−32x​−x−33​)=.....

Pertanyaan

limit as x rightwards arrow infinity of space open parentheses fraction numerator 2 x over denominator x minus 3 end fraction minus fraction numerator 3 over denominator x minus 3 end fraction close parentheses equals.....

  1. 1

  2. 2

  3. 3

  4. 4

  5. infinity

T. Prita

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Pada limit tak hingga berlaku:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space k over x to the power of n end cell equals 0 end table, dengan k equals text konstanta end text

Diketahui: table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of space open parentheses fraction numerator 2 x over denominator x minus 3 end fraction minus fraction numerator 3 over denominator x minus 3 end fraction close parentheses end cell end table

Selanjutnya membagi pembilang dan penyebut dengan variabel dengan pangkat tertinggi yaitu x yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space open parentheses fraction numerator 2 x over denominator x minus 3 end fraction minus fraction numerator 3 over denominator x minus 3 end fraction close parentheses end cell equals cell limit as x rightwards arrow infinity of space open parentheses fraction numerator 2 x minus 3 over denominator x minus 3 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 2 x over denominator x end fraction end style minus begin display style 3 over x end style over denominator begin display style x over x end style minus begin display style 3 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style 2 minus 3 over x end style over denominator begin display style 1 minus 3 over x end style end fraction end cell row blank equals cell fraction numerator begin display style limit as x rightwards arrow infinity of space 2 minus limit as x rightwards arrow infinity of space 3 over x end style over denominator begin display style limit as x rightwards arrow infinity of space 1 minus limit as x rightwards arrow infinity of space 3 over x end style end fraction end cell row blank equals cell fraction numerator 2 minus 0 over denominator 1 minus 0 end fraction end cell row blank equals cell 2 over 1 end cell row blank equals 2 end table

Oleh karena itu, jawaban yang benar adalah B.

87

4.6 (9 rating)

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