Pertanyaan

Nilai x → ∞ lim 3 + 4 x 4 2 + x 2 = ...

Nilai $x \to \infty lim \frac{4 2 + x ^{2}}{3 + 4 x} = ...$

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I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

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Pembahasan

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

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$\style{font-size:14px}{\mathrm{Nilai}}\style{font-size:14px}\;\underset{\style{font-size:14px}{\mathrm x}\style{font-size:14px}\rightarrow\style{font-size:14px}\infty}{\style{font-size:14px}\lim}\left(\sqrt{\style{font-size:14px}4\style{font-size:14px}{\mathrm x}^\style{font-size:14px}2\style{font-size:14px}\;\style{font-size:14px}+\style{font-size:14px}\;\style{font-size:14px}3\style{font-size:14px}{\mathrm x}\style{font-size:14px}\;\style{font-size:14px}+\style{font-size:14px}\;\style{font-size:14px}4}\style{font-size:14px}\;\style{font-size:14px}-\style{font-size:14px}\;\style{font-size:14px}2\style{font-size:14px}{\mathrm x}\style{font-size:14px}\;\style{font-size:14px}+\style{font-size:14px}1\right)\style{font-size:14px}\;\style{font-size:14px}=\style{font-size:14px}\;\style{font-size:14px}.\style{font-size:14px}.\style{font-size:14px}.\style{font-size:14px}.$

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