Pertanyaan

x → ∞ lim 2 x − 2 x + x 2 4 x + 3 adalah....

$x \to \infty lim \frac{4 x + 3}{2 x - 2 x + x ^{2}}$ adalah....

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I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

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$limit as x rightwards arrow infinity of fraction numerator 4 x plus 3 over denominator 2 x minus square root of 2 x plus x squared end root end fraction cross times open parentheses fraction numerator 2 x plus square root of 2 x plus x squared end root over denominator 2 x plus square root of 2 x plus x squared end root end fraction close parentheses equals limit as x rightwards arrow infinity of fraction numerator open parentheses 4 x plus 3 close parentheses begin display style open parentheses 2 x plus square root of 2 x plus x squared end root close parentheses end style over denominator 4 x squared minus open parentheses 2 x plus x squared close parentheses end fraction limit as equals x rightwards arrow infinity of fraction numerator 8 x squared plus 4 x square root of 2 x plus x squared end root plus 6 x plus 3 square root of 2 x plus x squared end root over denominator 3 x squared minus 2 x end fraction times open parentheses fraction numerator begin display style 1 over x squared end style over denominator begin display style 1 over x squared end style end fraction close parentheses equals limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 8 x squared over denominator x squared end fraction plus fraction numerator 4 x square root of 2 x plus x squared end root over denominator x squared end fraction plus fraction numerator 6 x over denominator x squared end fraction plus fraction numerator 3 square root of 2 x plus x squared end root over denominator x squared end fraction end style over denominator begin display style fraction numerator 3 x squared over denominator x squared end fraction minus fraction numerator 2 x over denominator x squared end fraction end style end fraction equals fraction numerator 8 plus 0 plus 0 plus 0 over denominator 3 minus 0 end fraction equals 8 over 3$