Pertanyaan

Nilai x → 0 lim 1 + 2 x − 1 − 2 x 4 x adalah ...

Nilai $x \to 0 lim \frac{4 x}{1 + 2 x - 1 - 2 x}$ adalah ...

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Habis dalam

Klaim

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

nilai .

nilai $limit as x rightwards arrow 0 of fraction numerator 4 x over denominator square root of 1 plus 2 x end root minus square root of 1 minus 2 x end root end fraction equals 2$ .

Pembahasan

Substitusi , diperoleh Karena hasilnya tidak terdefenisi, maka kita gunakan metode perkalian akar sekawan Jadi, nilai .

Substitusi x equals 0 , diperoleh

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

Karena hasilnya tidak terdefenisi, maka kita gunakan metode perkalian akar sekawan

$limit as x rightwards arrow 0 of fraction numerator 4 x over denominator square root of 1 plus 2 x end root minus square root of 1 minus 2 x end root end fraction equals limit as x rightwards arrow 0 of fraction numerator 4 x over denominator square root of 1 plus 2 x end root minus square root of 1 minus 2 x end root end fraction cross times fraction numerator square root of 1 plus 2 x end root plus square root of 1 minus 2 x end root over denominator square root of 1 plus 2 x end root plus square root of 1 minus 2 x end root end fraction equals limit as x rightwards arrow 0 of fraction numerator 4 x times open parentheses square root of 1 plus 2 x end root plus square root of 1 minus 2 x end root close parentheses over denominator open parentheses square root of 1 plus 2 x end root minus square root of 1 minus 2 x end root close parentheses times square root of 1 plus 2 x end root plus square root of 1 minus 2 x end root end fraction equals limit as x rightwards arrow 0 of fraction numerator 4 x open parentheses square root of 1 plus 2 x end root plus square root of 1 minus 2 x end root close parentheses over denominator open parentheses 1 plus 2 x close parentheses minus open parentheses 1 minus 2 x close parentheses end fraction equals limit as x rightwards arrow 0 of fraction numerator 4 x open parentheses square root of 1 plus 2 x end root plus square root of 1 minus 2 x end root close parentheses over denominator 4 x end fraction equals limit as x rightwards arrow 0 of open parentheses square root of 1 plus 2 x end root plus square root of 1 minus 2 x end root close parentheses equals square root of 1 plus 2 open parentheses 0 close parentheses end root plus square root of 1 minus 2 open parentheses 0 close parentheses end root equals square root of 1 plus square root of 1 equals 1 plus 1 equals 2$

Jadi, nilai $limit as x rightwards arrow 0 of fraction numerator 4 x over denominator square root of 1 plus 2 x end root minus square root of 1 minus 2 x end root end fraction equals 2$ .