Pertanyaan

lim x → 5 x − 1 − 2 6 − x − 1 − 2 + x − 1 = ....

$lim_{x \to 5} \frac{6 - x - 1 - 2 + x - 1}{x - 1 - 2} =$ ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi x = 5 , maka didapatkan hasil . Sehingga perlu dicari cara lain untuk mencari nilai limitnya. Perhatikan bahwa Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa jika dilakukan substitusi x = 5, maka didapatkan hasil .
Sehingga perlu dicari cara lain untuk mencari nilai limitnya.

Perhatikan bahwa

$begin mathsize 14px style limit as straight x rightwards arrow 5 of fraction numerator square root of 6 minus square root of straight x minus 1 end root end root minus square root of 2 plus square root of straight x minus 1 end root end root over denominator square root of straight x minus 1 end root minus 2 end fraction equals limit as straight x rightwards arrow 5 of open parentheses fraction numerator square root of 6 minus square root of straight x minus 1 end root end root minus square root of 2 plus square root of straight x minus 1 end root end root over denominator square root of straight x minus 1 end root minus 2 end fraction times fraction numerator square root of 6 minus square root of straight x minus 1 end root end root plus square root of 2 plus square root of straight x minus 1 end root end root over denominator square root of 6 minus square root of straight x minus 1 end root end root plus square root of 2 plus square root of straight x minus 1 end root end root end fraction close parentheses equals limit as straight x rightwards arrow 5 of fraction numerator open parentheses 6 minus square root of straight x minus 1 end root close parentheses minus open parentheses 2 plus square root of straight x minus 1 end root close parentheses over denominator open parentheses square root of straight x minus 1 end root minus 2 close parentheses open parentheses square root of 6 minus square root of straight x minus 1 end root end root plus square root of 2 plus square root of straight x minus 1 end root end root close parentheses end fraction equals limit as straight x rightwards arrow 5 of fraction numerator 4 minus 2 square root of straight x plus 1 end root over denominator open parentheses square root of straight x minus 1 end root minus 2 close parentheses open parentheses square root of 6 minus square root of straight x minus 1 end root end root plus square root of 2 plus square root of straight x minus 1 end root end root close parentheses end fraction equals limit as straight x rightwards arrow 5 of fraction numerator negative 2 open parentheses square root of straight x plus 1 end root minus 2 close parentheses over denominator open parentheses square root of straight x minus 1 end root minus 2 close parentheses open parentheses square root of 6 minus square root of straight x minus 1 end root end root plus square root of 2 plus square root of straight x minus 1 end root end root close parentheses end fraction equals limit as straight x rightwards arrow 5 of fraction numerator negative 2 over denominator square root of 6 minus square root of straight x minus 1 end root end root plus square root of 2 plus square root of straight x minus 1 end root end root end fraction equals fraction numerator negative 2 over denominator square root of 6 minus square root of 5 minus 1 end root end root plus square root of 2 plus square root of 5 minus 1 end root end root end fraction equals fraction numerator negative 2 over denominator square root of 6 minus square root of 4 end root plus square root of 2 plus square root of 4 end root end fraction equals fraction numerator negative 2 over denominator square root of 6 minus 2 end root plus square root of 2 plus 2 end root end fraction equals fraction numerator negative 2 over denominator square root of 4 plus square root of 4 end fraction equals fraction numerator negative 2 over denominator 2 plus 2 end fraction equals fraction numerator negative 2 over denominator 4 end fraction equals negative 1 half end style$

Jadi, jawaban yang tepat adalah D.