Pertanyaan

Nilai x → ∞ lim 3 x − 4 x 2 − 5 x + 6 2 x = ...

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

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Oleh karena itu, jawaban yang benar adalah B.

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

Oleh karena itu, jawaban yang benar adalah B.

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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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