Pertanyaan

x → ∞ lim ( 9 x 2 − 5 x − 2 − 3 x + 1 )

$x \to \infty lim (9 x^{2} - 5 x - 2 - 3 x + 1)$

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Jawaban terverifikasi

Jawaban

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limit as x rightwards arrow infinity of open parentheses square root of 9 x squared minus 5 x minus 2 end root minus 3 x plus 1 close parentheses equals 1 over 6

Pembahasan

Jadi, .

$begin mathsize 12px style 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 9 x squared minus 5 x minus 2 end root minus 3 x plus 1 close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open parentheses square root of 9 x squared minus 5 x minus 2 end root minus open parentheses 3 x minus 1 close parentheses close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of open square brackets open square brackets square root of 9 x squared minus 5 x minus 2 end root minus open parentheses 3 x minus 1 close parentheses close square brackets times fraction numerator square root of 9 x squared minus 5 x minus 2 end root plus open parentheses 3 x minus 1 close parentheses over denominator square root of 9 x squared minus 5 x minus 2 end root plus open parentheses 3 x minus 1 close parentheses end fraction close square brackets end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open square brackets open parentheses 9 x squared minus 5 x minus 2 close parentheses minus open parentheses 3 x minus 1 close parentheses squared close square brackets over denominator square root of 9 x squared minus 5 x minus 2 end root plus open parentheses 3 x minus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 9 x squared minus 5 x minus 2 minus open parentheses 9 x squared minus 6 x plus 1 close parentheses over denominator square root of 9 x squared minus 5 x minus 2 end root plus open parentheses 3 x minus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 9 x squared minus 9 x squared minus 5 x plus 6 x minus 2 minus 1 over denominator square root of 9 x squared minus 5 x minus 2 end root plus open parentheses 3 x minus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x minus 3 over denominator square root of 9 x squared minus 5 x minus 2 end root plus open parentheses 3 x minus 1 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style x over x end style minus begin display style 3 over x end style over denominator square root of begin display style fraction numerator 9 x squared over denominator x squared end fraction end style minus begin display style fraction numerator 5 x over denominator x squared end fraction end style minus begin display style 2 over x squared end style end root plus open parentheses begin display style fraction numerator 3 x over denominator x end fraction end style minus begin display style 1 over x end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 1 minus 3 over x end style over denominator square root of begin display style 9 minus 5 over x minus 2 over x squared end style end root plus open parentheses begin display style 3 minus 1 over x end style close parentheses end fraction end cell row blank equals cell fraction numerator 1 minus 0 over denominator square root of 9 minus 0 minus 0 end root plus open parentheses 3 minus 0 close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 9 plus 3 end fraction end cell row blank equals cell fraction numerator 1 over denominator 3 plus 3 end fraction end cell row blank equals cell 1 over 6 end cell end table end style$

Jadi, limit as x rightwards arrow infinity of open parentheses square root of 9 x squared minus 5 x minus 2 end root minus 3 x plus 1 close parentheses equals 1 over 6 .

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