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Nilai begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of 2 x squared plus 4 x plus 3 end root minus square root of 2 x plus x plus 1 end root close parentheses equals end style....

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

hasil dari limit tersebut yaitu begin mathsize 14px style square root of 2 end style.

Pembahasan

Limit tak hingga dapat diselesaikan dengan membagi semua suku dengan variabel yang memiliki pangkat tertinggi. Kemudian substitusi semua variabel dengan tak hingga.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of 2 x squared plus 4 x plus 3 end root minus square root of 2 x plus x plus 1 end root close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses square root of 2 x squared plus 4 x plus 3 end root minus square root of 2 x plus x plus 1 end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of fraction numerator 2 x squared over denominator x squared end fraction plus fraction numerator 4 x over denominator x squared end fraction plus 3 over x squared end root minus square root of fraction numerator 2 x over denominator x squared end fraction plus x over x squared plus 1 over x squared end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 2 plus 4 over x plus 3 over x squared end root minus square root of 2 over x plus 1 over x plus 1 over x squared end root close parentheses end cell row blank equals cell square root of 2 plus 4 over infinity plus 3 over infinity squared end root minus square root of 2 over infinity plus 1 over infinity plus 1 over infinity squared end root end cell row blank equals cell square root of 2 plus 0 plus 0 end root minus square root of 0 plus 0 plus 0 end root end cell row blank equals cell square root of 2 minus 0 end cell row blank equals cell square root of 2 end cell end table end style

Jadi, hasil dari limit tersebut yaitu begin mathsize 14px style square root of 2 end style.

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