Pertanyaan

x → ∞ lim x ( 4 x + 5 ) − 4 x 2 − 3

$x \to \infty lim x (4 x + 5) - 4 x^{2} - 3$

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

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Pembahasan

Untuk menyelesaian limit tak hingga bentuk akar berlaku: Jadi,

Untuk menyelesaian limit tak hingga bentuk akar berlaku:

$begin mathsize 14px style limit as x rightwards arrow infinity of square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus c end root equals straight L straight L equals negative infinity space left right double arrow space a less than p straight L equals fraction numerator b minus q over denominator 2 square root of a end fraction space left right double arrow space a equals p straight L equals infinity space left right double arrow space a greater than p end style$

$begin mathsize 14px style limit as x rightwards arrow infinity of square root of x left parenthesis 4 x plus 5 right parenthesis end root minus square root of 4 x squared minus 3 end root equals limit as x rightwards arrow infinity of square root of 4 x squared plus 5 x end root minus square root of 4 x squared minus 3 end root equals fraction numerator b minus q over denominator 2 square root of a end fraction space space equals fraction numerator 5 minus 0 over denominator 2 square root of 4 end fraction equals fraction numerator 5 over denominator 2 times 2 end fraction equals 5 over 4 end style$

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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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