Pertanyaan

x → ∞ lim ( 2 x − 5 4 x 2 − 12 x + 9 ) = ...

$x \to \infty lim (2 x - 5 4 x^{2} - 12 x + 9) = ...$

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I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Jika a = p maka bentuk limit tak hingga berikut adalah: Maka, Jawaban A

Jika a = p maka bentuk limit tak hingga berikut adalah:

$limit as x rightwards arrow infinity of square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root equals fraction numerator b minus q over denominator 2 square root of a end fraction$

Maka,

$limit as x rightwards arrow infinity of open parentheses 2 x minus 5 close parentheses minus square root of 4 x squared minus 12 x plus 9 end root equals limit as x rightwards arrow infinity of square root of open parentheses 2 x minus 5 close parentheses squared end root minus square root of 4 x squared minus 12 x plus 9 end root equals limit as x rightwards arrow infinity of square root of 4 x squared minus 20 x plus 25 end root minus square root of 4 x squared minus 12 x plus 9 end root equals fraction numerator negative 20 minus open parentheses negative 12 close parentheses over denominator 2 square root of 4 end fraction equals negative 8 over 4 equals negative 2$

Jawaban A

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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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