Pertanyaan

x → ∞ lim ( 25 x 2 − 10 x + 1 − 25 x 2 + 5 x − 7 ) = ....

$x \to \infty lim (25 x^{2} - 10 x + 1 - 25 x^{2} + 5 x - 7) = ....$

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Jawaban

nilai

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of 25 x squared minus 10 x plus 1 end root minus square root of 25 x squared plus 5 x minus 7 end root close parentheses end cell equals cell negative 3 over 2 end cell end table

Pembahasan

Jika ada maka hasil limitnya adalah sehingga Jadi nilai

Jika ada limit as x rightwards arrow infinity of square root of a x plus b x plus c end root minus square root of p x squared plus q x plus r end root maka hasil limitnya adalah $fraction numerator b minus q over denominator 2 square root of a end fraction$ sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of 25 x squared minus 10 x plus 1 end root minus square root of 25 x squared plus 5 x minus 7 end root close parentheses end cell equals cell fraction numerator negative 10 minus 5 over denominator 2 square root of 25 end fraction end cell row blank equals cell fraction numerator negative 15 over denominator 2 cross times 5 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator 2 end fraction end cell row blank equals cell negative 3 over 2 end cell end table$

Jadi nilai table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of 25 x squared minus 10 x plus 1 end root minus square root of 25 x squared plus 5 x minus 7 end root close parentheses end cell equals cell negative 3 over 2 end cell end table

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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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