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Pertanyaan

Nilai begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator 4 x squared minus 64 over denominator x plus square root of x minus 6 end fraction end style adalah ....

  1. begin mathsize 14px style 128 over 5 end style   

  2. begin mathsize 14px style 64 over 5 end style 

  3. begin mathsize 14px style 32 over 5 end style 

  4. undefined 

  5. begin mathsize 14px style 8 over 5 end style 

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Dengan menggunakan metode L'hospital.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of fraction numerator 4 x squared minus 64 over denominator x plus square root of x minus 6 end fraction end cell equals cell limit as x rightwards arrow 4 of fraction numerator 4 x squared minus 64 over denominator x plus x to the power of begin display style 1 half end style end exponent minus 6 end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator 8 x minus 0 over denominator 1 plus begin display style 1 half end style x to the power of begin display style negative 1 half end style end exponent minus 0 end fraction end cell row blank equals cell limit as x rightwards arrow 4 of fraction numerator 8 x over denominator 1 plus fraction numerator 1 over denominator 2 square root of x end fraction end fraction end cell row blank equals cell fraction numerator 8 times 4 over denominator 1 plus fraction numerator 1 over denominator 2 square root of 4 end fraction end fraction end cell row blank equals cell fraction numerator 32 over denominator 1 plus begin display style 1 fourth end style end fraction end cell row blank equals cell fraction numerator 32 over denominator begin display style 5 over 4 end style end fraction end cell row blank equals cell 32 divided by 5 over 4 end cell row blank equals cell 32 cross times 4 over 5 end cell row blank equals cell 128 over 5 end cell end table end style 

Jadi, jawaban yang tepat adalah A.

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