Pertanyaan

Nilai dari x → ∞ lim ( 81 x 2 − 10 x + 15 − 9 x + 1 ) = ....

Nilai dari $x \to \infty lim (81 x^{2} - 10 x + 15 - 9 x + 1) = ....$

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Jawaban terverifikasi

Jawaban

nilai limitnya adalah

nilai limitnya adalah 4 over 9

Pembahasan

Diperhatikan bahwa Maka Jadi, nilai limitnya adalah

Diperhatikan bahwa

$limit as x rightwards arrow infinity of open parentheses square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root close parentheses equals open curly brackets table attributes columnalign left end attributes row cell table row cell infinity comma space space jika space a greater than p end cell row cell fraction numerator b minus q over denominator 2 square root of a end fraction comma space jika space a equals p end cell end table end cell row cell negative infinity comma space jika space a less than p end cell end table close$

Maka

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of open parentheses square root of 81 x squared minus 10 x plus 15 end root minus 9 x plus 1 close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 81 x squared minus 10 x plus 15 end root minus open parentheses 9 x minus 1 close parentheses close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 81 x squared minus 10 x plus 15 end root minus square root of open parentheses 9 x minus 1 close parentheses squared end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 81 x squared minus 10 x plus 15 end root minus square root of 81 x squared minus 18 x plus 1 end root close parentheses end cell row blank equals cell fraction numerator negative 10 minus left parenthesis negative 18 right parenthesis over denominator 2 square root of 81 end fraction end cell row blank equals cell 8 over 18 end cell row blank equals cell 4 over 9 end cell end table$

Jadi, nilai limitnya adalah 4 over 9

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