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Pertanyaan

x → ∞ lim ​ ( 3 x ​ ) ( 3 x + 2 ​ − 3 x − 1 ​ ) =

  

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N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

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Pembahasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of square root of ax squared plus bx plus straight c end root minus square root of px squared plus qx plus straight c end root end cell row straight a equals cell straight p rightwards arrow fraction numerator straight b minus straight q over denominator 2 square root of straight a end fraction end cell row blank blank blank row blank blank cell limit as straight x rightwards arrow infinity of left parenthesis square root of 3 straight x end root right parenthesis left parenthesis square root of 3 straight x plus 2 end root minus square root of 3 straight x minus 1 end root right parenthesis end cell row blank equals cell limit as straight x rightwards arrow infinity of left parenthesis square root of 3 straight x end root right parenthesis left parenthesis square root of 3 straight x plus 2 end root right parenthesis minus left parenthesis square root of 3 straight x end root right parenthesis left parenthesis square root of 3 straight x minus 1 end root right parenthesis end cell row blank equals cell limit as straight x rightwards arrow infinity of left parenthesis square root of left parenthesis 3 straight x right parenthesis open parentheses 3 straight x plus 2 close parentheses end root square root of open parentheses 3 straight x close parentheses open parentheses 3 straight x minus 1 close parentheses end root end cell row blank equals cell limit as straight x rightwards arrow infinity of left parenthesis square root of 9 straight x squared plus 6 straight x end root minus square root of 9 straight x squared minus 3 straight x end root end cell row blank equals cell fraction numerator 6 minus left parenthesis negative 3 right parenthesis over denominator 2 square root of 9 end fraction end cell row blank equals cell fraction numerator 6 plus 3 over denominator 2 times 3 end fraction end cell row blank equals cell 9 over 6 end cell row blank equals cell 3 over 2 end cell end table end style 

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