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x→∞lim​3x+9x2−5x+7​x−5​=...

Pertanyaan

limit as x rightwards arrow infinity of fraction numerator x minus 5 over denominator 3 x plus square root of 9 x squared minus 5 x plus 7 end root end fraction equals...         

  1. 1 half  

  2. 1 third 

  3. 1 fourth 

  4. 1 fifth 

  5. 1 over 6 

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Ingat! 

limit as x rightwards arrow infinity of open parentheses c over x to the power of n close parentheses equals 0    

Perhatikan perhitungan berikut! 

limit as x rightwards arrow infinity of fraction numerator x minus 5 over denominator 3 x plus square root of 9 x squared minus 5 x plus 7 end root end fraction equals limit as x rightwards arrow infinity of open parentheses fraction numerator x minus 5 over denominator 3 x plus square root of 9 x squared minus 5 x plus 7 end root end fraction close parentheses times fraction numerator open parentheses begin display style 1 over x end style close parentheses over denominator open parentheses begin display style 1 over x end style close parentheses end fraction equals limit as x rightwards arrow infinity of open parentheses fraction numerator 1 minus begin display style 5 over x end style over denominator 3 plus begin display style fraction numerator square root of 9 x squared minus 5 x plus 7 end root over denominator x end fraction end style end fraction close parentheses equals limit as x rightwards arrow infinity of open parentheses fraction numerator 1 minus begin display style 5 over x end style over denominator 3 plus begin display style square root of fraction numerator 9 x squared minus 5 x plus 7 over denominator x squared end fraction end root end style end fraction close parentheses equals limit as x rightwards arrow infinity of open parentheses fraction numerator 1 minus begin display style 5 over x end style over denominator 3 plus begin display style square root of 9 minus 5 over x plus 7 over x squared end root end style end fraction close parentheses equals fraction numerator 1 minus 0 over denominator 3 plus square root of 9 minus 0 plus 0 end root end fraction equals fraction numerator 1 over denominator 3 plus 3 end fraction equals 1 over 6              

Oleh karena itu, jawaban yang benar adalah E.

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