Pertanyaan

x → 6 lim 6 − 5 x + 6 x − 2 − 10 − x

$x \to 6 lim \frac{x - 2 - 10 - x}{6 - 5 x + 6}$

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Habis dalam

Klaim

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai $begin mathsize 14px style limit as x rightwards arrow 6 of fraction numerator square root of x minus 2 end root minus square root of 10 minus x end root over denominator 6 minus square root of 5 x plus 6 end root end fraction end style$ adalah

Pembahasan

Menyelesaikan limit dengan mengalikan akar sekawan, diperoleh Jadi, nilai adalah .

Menyelesaikan limit dengan mengalikan akar sekawan, diperoleh

$begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 6 of fraction numerator square root of x minus 2 end root minus square root of 10 minus x end root over denominator 6 minus square root of 5 x plus 6 end root end fraction end cell equals cell limit as x rightwards arrow 6 of fraction numerator square root of x minus 2 end root minus square root of 10 minus x end root over denominator 6 minus square root of 5 x plus 6 end root end fraction times fraction numerator 6 plus square root of 5 x plus 6 end root over denominator 6 plus square root of 5 x plus 6 end root end fraction end cell row blank equals cell limit as x rightwards arrow 6 of fraction numerator left parenthesis square root of x minus 2 end root minus square root of 10 minus x end root right parenthesis left parenthesis 6 plus square root of 5 x plus 6 end root right parenthesis over denominator 36 minus left parenthesis 5 x plus 6 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 6 of fraction numerator left parenthesis square root of x minus 2 end root minus square root of 10 minus x end root right parenthesis left parenthesis 6 plus square root of 5 x plus 6 end root right parenthesis over denominator left parenthesis 30 minus 5 x right parenthesis end fraction times fraction numerator left parenthesis square root of x minus 2 end root plus square root of 10 minus x end root right parenthesis over denominator left parenthesis square root of x minus 2 end root plus square root of 10 minus x end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 6 of fraction numerator left parenthesis 6 plus square root of 5 x plus 6 end root right parenthesis left parenthesis x minus 2 minus 10 plus x right parenthesis over denominator left parenthesis 30 minus 5 x right parenthesis left parenthesis square root of x minus 2 end root plus square root of 10 minus x end root right parenthesis end fraction end cell row blank blank blank row blank equals cell limit as x rightwards arrow 6 of fraction numerator left parenthesis 6 plus square root of 5 x plus 6 end root right parenthesis 2 left parenthesis x minus 6 right parenthesis over denominator negative 5 left parenthesis x minus 6 right parenthesis left parenthesis square root of x minus 2 end root plus square root of 10 minus x end root right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 6 of fraction numerator left parenthesis 6 plus square root of 5 x plus 6 end root right parenthesis 2 over denominator negative 5 left parenthesis square root of x minus 2 end root plus square root of 10 minus x end root right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis 6 plus square root of 5 times 6 plus 6 end root right parenthesis 2 over denominator negative 5 left parenthesis square root of 6 minus 2 end root plus square root of 10 minus 6 end root right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis 6 plus 6 right parenthesis 2 over denominator negative 5 left parenthesis 2 plus 2 right parenthesis end fraction end cell row blank equals cell fraction numerator 24 over denominator negative 20 end fraction end cell row blank equals cell negative 6 over 5 end cell end table end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow 6 of fraction numerator square root of x minus 2 end root minus square root of 10 minus x end root over denominator 6 minus square root of 5 x plus 6 end root end fraction end style$ adalah .