Pertanyaan

Nilai x → 6 lim x − 6 3 x − 2 − 2 x + 4 = ...

Nilai $x \to 6 lim \frac{3 x - 2 - 2 x + 4}{x - 6} = ...$

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Klaim

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

Nilai adalah

Nilai $limit as x rightwards arrow 6 of fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction$ adalah 1 over 8

Pembahasan

Untuk menyelesaikan fungsi limit di atas dapat menggunakan konsep mengalikan dengan akar sekawan, sehinga: Jadi, Nilai adalah

Untuk menyelesaikan fungsi limit di atas dapat menggunakan konsep mengalikan dengan akar sekawan, sehinga:

$limit as x rightwards arrow 6 of fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction equals$

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 6 of fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction cross times fraction numerator square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root over denominator square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root end fraction end cell row blank equals cell limit as x rightwards arrow 6 of fraction numerator open parentheses square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root close parentheses open parentheses square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root close parentheses over denominator left parenthesis x minus 6 right parenthesis open parentheses square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 6 of fraction numerator 3 x minus 2 minus open parentheses 2 x plus 4 close parentheses over denominator left parenthesis x minus 6 right parenthesis open parentheses square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 6 of fraction numerator x minus 6 over denominator left parenthesis x minus 6 right parenthesis open parentheses square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 6 of fraction numerator 1 over denominator open parentheses square root of 3 x minus 2 end root plus square root of 2 x plus 4 end root close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator open parentheses square root of 3 open parentheses 6 close parentheses minus 2 end root plus square root of 2 open parentheses 6 close parentheses plus 4 end root close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 16 plus square root of 16 end fraction end cell row blank equals cell 1 over 8 end cell end table$

Jadi, Nilai $limit as x rightwards arrow 6 of fraction numerator square root of 3 x minus 2 end root minus square root of 2 x plus 4 end root over denominator x minus 6 end fraction$ adalah 1 over 8