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x → ∞ lim ​ ( x + 6 x ​ ​ − x − 2 x ​ ​ )

  

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A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

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nilai adalah .

nilai begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of x plus 6 square root of x end root minus square root of x minus 2 square root of x end root close parentheses end style adalah begin mathsize 14px style 4 end style.

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Pembahasan

Menyelesaikan limit dengan mengalikan akar sekawan dan membagi semua suku dengan variabel yng memiliki pangkat tertinggi pada penyebut, dalam kasus ini , diperoleh Jadi, nilai adalah .

Menyelesaikan limit dengan mengalikan akar sekawan dan membagi semua suku dengan variabel yng memiliki pangkat tertinggi pada penyebut, dalam kasus ini begin mathsize 14px style square root of x end style, diperoleh

begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of x plus 6 square root of x end root minus square root of x minus 2 square root of x end root close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses square root of x plus 6 square root of x end root minus square root of x minus 2 square root of x end root close parentheses times fraction numerator square root of x plus 6 square root of x end root plus square root of x minus 2 square root of x end root over denominator square root of x plus 6 square root of x end root plus square root of x minus 2 square root of x end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x plus 6 square root of x minus x plus 2 square root of x over denominator square root of x plus 6 square root of x end root plus square root of x minus 2 square root of x end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 8 square root of x over denominator square root of x plus 6 square root of x end root plus square root of x minus 2 square root of x end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 8 square root of x over denominator square root of x end fraction end style over denominator begin display style fraction numerator square root of x plus 6 square root of x end root over denominator square root of x end fraction end style plus begin display style fraction numerator square root of x minus 2 square root of x end root over denominator square root of x end fraction end style end fraction end cell row blank equals cell fraction numerator 8 over denominator square root of begin display style fraction numerator x plus 6 square root of x over denominator x end fraction end style end root plus square root of fraction numerator x minus 2 square root of x over denominator x end fraction end root end fraction end cell row blank equals cell fraction numerator 8 over denominator square root of begin display style 1 plus 0 end style end root plus square root of 1 minus 0 end root end fraction end cell row blank equals cell fraction numerator 8 over denominator 1 plus 1 end fraction end cell row blank equals cell 8 over 2 end cell row blank equals 4 end table end style 

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses square root of x plus 6 square root of x end root minus square root of x minus 2 square root of x end root close parentheses end style adalah begin mathsize 14px style 4 end style.

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