Pertanyaan

x → ∞ lim 9 x 2 + 5 − 4 x 2 − 6 x 2 − 4 + x 2 + 3

$x \to \infty lim \frac{x ^{2} - 4 + x ^{2} + 3}{9 x ^{2} + 5 - 4 x ^{2} - 6}$

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A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator square root of x squared minus 4 end root plus square root of x squared plus 3 end root over denominator square root of 9 x squared plus 5 end root minus square root of 4 x squared minus 6 end root end fraction end style$ adalah

Pembahasan

Menyelesaikan limit dengan cara membagi semua suku dengan variabel yng memiliki pangkat tertinggi pada penyebut, dalam kasus ini . Untuk , diperoleh Jadi, nilai adalah .

Menyelesaikan limit dengan cara membagi semua suku dengan variabel yng memiliki pangkat tertinggi pada penyebut, dalam kasus ini .

Untuk $begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator square root of x squared minus 4 end root plus square root of x squared plus 3 end root over denominator square root of 9 x squared plus 5 end root minus square root of 4 x squared minus 6 end root end fraction end style$ , diperoleh

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator square root of x squared minus 4 end root plus square root of x squared plus 3 end root over denominator square root of 9 x squared plus 5 end root minus square root of 4 x squared minus 6 end root end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator square root of x squared minus 4 end root over denominator square root of x squared end root end fraction end style plus begin display style fraction numerator square root of x squared plus 3 end root over denominator square root of x squared end root end fraction end style over denominator begin display style fraction numerator square root of 9 x squared plus 5 end root over denominator square root of x squared end root end fraction end style minus begin display style fraction numerator square root of 4 x squared minus 6 end root over denominator square root of x squared end root end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator square root of begin display style x squared over x squared end style minus begin display style 4 over x squared end style end root plus square root of begin display style x squared over x squared end style plus begin display style 3 over x squared end style end root over denominator square root of begin display style fraction numerator 9 x squared over denominator x squared end fraction end style plus begin display style 5 over x squared end style end root minus square root of begin display style fraction numerator 4 x squared over denominator x squared end fraction end style minus begin display style 6 over x squared end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator square root of begin display style 1 minus 0 end style end root plus square root of begin display style 1 plus 0 end style end root over denominator square root of begin display style 9 plus 0 end style end root minus square root of begin display style 4 minus 0 end style end root end fraction end cell row blank equals cell fraction numerator square root of begin display style 1 end style end root plus square root of begin display style 1 end style end root over denominator square root of begin display style 9 end style end root minus square root of begin display style 4 end style end root end fraction end cell row blank equals cell fraction numerator 1 plus 1 over denominator 3 minus 2 end fraction end cell row blank equals 2 end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator square root of x squared minus 4 end root plus square root of x squared plus 3 end root over denominator square root of 9 x squared plus 5 end root minus square root of 4 x squared minus 6 end root end fraction end style$ adalah .

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