Pertanyaan

Nilai x → 3 lim 2 x − 3 − x x + 2 − 2 x − 1 adalah....

Nilai $x \to 3 lim \frac{x + 2 - 2 x - 1}{2 x - 3 - x}$ adalah....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Nilai limit pada soal di atas dapat dicari dengan cara mengalikannya dengan akar sekawan dari yaitu . Diperoleh Jadi, jawaban yang tepat adalah B.

Nilai limit pada soal di atas dapat dicari dengan cara mengalikannya dengan akar sekawan dari yaitu . Diperoleh

$begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator square root of 2 x minus 3 end root minus square root of x end fraction equals limit as x rightwards arrow 3 of open parentheses fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator square root of 2 x minus 3 end root minus square root of x end fraction times fraction numerator square root of 2 x minus 3 end root plus square root of x over denominator square root of 2 x minus 3 end root plus square root of x end fraction close parentheses equals limit as x rightwards arrow 3 of open parentheses fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator x minus 3 end fraction times square root of 2 x minus 3 end root plus square root of x close parentheses equals limit as x rightwards arrow 3 of fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator x minus 3 end fraction times limit as x rightwards arrow 3 of square root of 2 x minus 3 end root plus square root of x equals limit as x rightwards arrow 3 of fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator x minus 3 end fraction times 2 square root of 3 equals 2 square root of 3 open parentheses limit as x rightwards arrow 3 of fraction numerator square root of x plus 2 end root minus square root of 2 x minus 1 end root over denominator x minus 3 end fraction times fraction numerator square root of x plus 2 end root plus square root of 2 x minus 1 end root over denominator square root of x plus 2 end root plus square root of 2 x minus 1 end root end fraction close parentheses equals 2 square root of 3 open parentheses limit as x rightwards arrow 3 of fraction numerator negative x plus 3 over denominator x minus 3 end fraction times fraction numerator 1 over denominator square root of x plus 2 end root plus square root of 2 x minus 1 end root end fraction close parentheses equals negative 2 square root of 3 limit as x rightwards arrow 3 of fraction numerator 1 over denominator square root of x plus 2 end root plus square root of 2 x minus 1 end root end fraction equals negative 2 square root of 3 times fraction numerator 1 over denominator square root of 5 plus square root of 5 end fraction equals negative fraction numerator 2 square root of 3 over denominator 2 square root of 5 end fraction equals negative square root of 3 over 5 end root equals negative 1 fifth square root of 15 end style$

Jadi, jawaban yang tepat adalah B.