Pertanyaan

x → ∞ lim 10 x − 4 4 x 2 + 2 x + 9 x 2 − 16 = ...

$x \to \infty lim \frac{4 x ^{2} + 2 x + 9 x ^{2} - 16}{10 x - 4} = ...$

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A. Nadhira

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$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 fraction numerator square root of 4 x squared plus 2 x end root plus square root of 9 x squared minus 16 end root over denominator 10 x minus 4 end fraction open parentheses fraction numerator begin display style 1 over x end style over denominator begin display style 1 over x end style end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style square root of 4 x squared plus 2 x end root open parentheses fraction numerator begin display style 1 end style over denominator begin display style x end style end fraction close parentheses plus square root of 9 x squared minus 16 end root open parentheses fraction numerator begin display style 1 end style over denominator begin display style x end style end fraction close parentheses end style over denominator begin display style open parentheses 10 x minus 4 close parentheses open parentheses fraction numerator begin display style 1 end style over denominator begin display style x end style end fraction close parentheses end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style square root of fraction numerator 4 x squared plus 2 x over denominator x squared end fraction end root plus square root of fraction numerator 9 x squared minus 16 over denominator x squared end fraction end root end style over denominator begin display style 10 minus 4 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style square root of 4 plus 2 over x end root plus square root of 9 minus 16 over x squared end root end style over denominator begin display style 10 minus 4 over x end style end fraction end cell row blank equals cell fraction numerator square root of 4 begin display style plus end style begin display style square root of 9 end style over denominator 10 end fraction end cell row blank equals cell 5 over 10 end cell row blank equals cell 1 half end cell end table end style$