Pertanyaan

Hasil dari x → 0 lim 9 − 2 x − 9 − 4 x x + 4 − 3 x + 4 adalah ....

Hasil dari $x \to 0 lim \frac{x + 4 - 3 x + 4}{9 - 2 x - 9 - 4 x}$ adalah ....

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R. Mahmudah

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan perhitungan berikut! Jadi, jawaban yang tepat adalah A.

Perhatikan perhitungan berikut!

$begin mathsize 11px style limit as x rightwards arrow 0 of fraction numerator square root of x plus 4 end root minus square root of 3 x plus 4 end root over denominator square root of 9 minus 2 x end root minus square root of 9 minus 4 x end root end fraction equals limit as x rightwards arrow 0 of open parentheses fraction numerator square root of x plus 4 end root minus square root of 3 x plus 4 end root over denominator square root of 9 minus 2 x end root minus square root of 9 minus 4 x end root end fraction times fraction numerator square root of x plus 4 end root plus square root of 3 x plus 4 end root over denominator square root of x plus 4 end root plus square root of 3 x plus 4 end root end fraction times fraction numerator square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root over denominator square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root end fraction close parentheses equals limit as x rightwards arrow 0 of open parentheses fraction numerator open parentheses square root of x plus 4 end root minus square root of 3 x plus 4 end root close parentheses open parentheses square root of x plus 4 end root plus square root of 3 x plus 4 end root close parentheses over denominator open parentheses square root of 9 minus 2 x end root minus square root of 9 minus 4 x end root close parentheses open parentheses square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root close parentheses end fraction times fraction numerator square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root over denominator square root of x plus 4 end root plus square root of 3 x plus 4 end root end fraction close parentheses equals limit as x rightwards arrow 0 of open parentheses fraction numerator open parentheses x plus 4 close parentheses minus open parentheses 3 x plus 4 close parentheses over denominator open parentheses 9 minus 2 x close parentheses minus open parentheses 9 minus 4 x close parentheses end fraction times fraction numerator square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root over denominator square root of x plus 4 end root plus square root of 3 x plus 4 end root end fraction close parentheses equals limit as x rightwards arrow 0 of open parentheses fraction numerator negative 2 x over denominator 2 x end fraction times fraction numerator square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root over denominator square root of x plus 4 end root plus square root of 3 x plus 4 end root end fraction close parentheses equals limit as x rightwards arrow 0 of open parentheses open parentheses negative 1 close parentheses times fraction numerator square root of 9 minus 2 x end root plus square root of 9 minus 4 x end root over denominator square root of x plus 4 end root plus square root of 3 x plus 4 end root end fraction close parentheses equals left parenthesis negative 1 right parenthesis times fraction numerator square root of 9 minus 2 times 0 end root plus square root of 9 minus 4 times 0 end root over denominator square root of 0 plus 4 end root plus square root of 3 times 0 plus 4 end root end fraction equals negative fraction numerator square root of 9 plus square root of 9 over denominator square root of 4 plus square root of 4 end fraction equals negative fraction numerator 3 plus 3 over denominator 2 plus 2 end fraction equals negative 6 over 4 equals negative 3 over 2 end style$

Jadi, jawaban yang tepat adalah A.