Pertanyaan

Nilai x → − 2 lim x 2 − x − 6 x + 6 − 2 = ....

Nilai $x \to - 2 lim \frac{x + 6 - 2}{x ^{2} - x - 6} = ....$

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N. Putri

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

nilai

nilai $limit as x rightwards arrow negative 2 of fraction numerator square root of x plus 6 end root minus 2 over denominator x squared minus x minus 6 end fraction equals negative 1 over 20.$

Pembahasan

Untuk menyelesaikan limit tersebut, gunakan pengali faktor sekawan, dan diperoleh : Jadi, nilai

Untuk menyelesaikan limit tersebut, gunakan pengali faktor sekawan, dan diperoleh :

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 2 of fraction numerator square root of x plus 6 end root minus 2 over denominator x squared minus x minus 6 end fraction end cell equals cell space limit as x rightwards arrow negative 2 of fraction numerator square root of x plus 6 end root minus 2 over denominator x squared minus x minus 6 end fraction cross times fraction numerator square root of x plus 6 end root plus 2 over denominator square root of x plus 6 end root plus 2 end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator x plus 2 over denominator left parenthesis x squared minus x minus 6 right parenthesis left parenthesis square root of x plus 6 end root plus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator x plus 2 over denominator left parenthesis x plus 2 right parenthesis left parenthesis x minus 3 right parenthesis left parenthesis square root of x plus 6 end root plus 2 right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow negative 2 of fraction numerator 1 over denominator left parenthesis x minus 3 right parenthesis left parenthesis square root of x plus 6 end root plus 2 right parenthesis end fraction end cell row blank equals cell fraction numerator 1 over denominator left parenthesis negative 2 minus 3 right parenthesis left parenthesis square root of negative 2 plus 6 end root plus 2 right parenthesis end fraction end cell row blank equals cell negative 1 over 20 end cell end table$

Jadi, nilai $limit as x rightwards arrow negative 2 of fraction numerator square root of x plus 6 end root minus 2 over denominator x squared minus x minus 6 end fraction equals negative 1 over 20.$