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Pertanyaan

Nilai dari begin mathsize 14px style limit as x rightwards arrow infinity of square root of 4 x squared minus 3 x plus 7 end root minus open parentheses 2 x minus 3 close parentheses end style adalah...

  1. begin mathsize 14px style negative 3 3 over 4 end style

  2. begin mathsize 14px style negative 2 1 fourth end style

  3. begin mathsize 14px style 0 end style

  4. begin mathsize 14px style 2 1 fourth end style

  5. begin mathsize 14px style infinity end style

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat kembali cara cepat untuk menentukan nilai imit tak hingga bentuk akar berikut.

limit as x rightwards arrow infinity of space square root of a x squared plus b x plus c end root minus square root of a x squared plus p x plus q end root equals fraction numerator b minus p over denominator 2 square root of a end fraction

Sehingga semua bentuk pada soal harus diubah menjadi bentuk akar.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell limit as x rightwards arrow infinity of square root of 4 x squared minus 3 x plus 7 end root minus left parenthesis 2 x minus 3 right parenthesis end cell row blank equals cell limit as x rightwards arrow infinity of square root of 4 x squared minus 3 x plus 7 end root minus square root of open parentheses 2 x minus 3 close parentheses squared end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of 4 x squared minus 3 x plus 7 end root minus square root of open parentheses 2 x minus 3 close parentheses open parentheses 2 x minus 3 close parentheses end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of 4 x squared minus 3 x plus 7 end root minus square root of 4 x squared minus 6 x minus 6 x plus 9 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of 4 x squared minus 3 x plus 7 end root minus square root of 4 x squared minus 12 x plus 9 end root end cell row blank equals cell fraction numerator negative 3 minus open parentheses negative 12 close parentheses over denominator 2 square root of 4 end fraction end cell row blank equals cell fraction numerator negative 3 plus 12 over denominator 2 times 2 end fraction end cell row blank equals cell 9 over 4 end cell row blank equals cell 2 1 fourth end cell end table end cell end table 

Sehingga diperoleh nilai limit as x rightwards arrow infinity of square root of 4 x squared minus 3 x plus 7 end root minus open parentheses 2 x minus 3 close parentheses equals 2 1 fourth.

Oleh karena itu, jawaban yang benar adalah D.

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