Pertanyaan

lim x → 4 3 − x + 5 4 − x + 5 − x + 5 − 2 = ....

$lim_{x \to 4} \frac{4 - x + 5 - x + 5 - 2}{3 - x + 5} =$ ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi x = 4 , maka didapatkan hasil . Sehingga perlu dicari cara lain untuk mencari nilai limitnya. Perhatikan bahwa Jadi, jawaban yang tepat adalah C.

Perhatikan bahwa jika dilakukan substitusi x = 4, maka didapatkan hasil .
Sehingga perlu dicari cara lain untuk mencari nilai limitnya.

Perhatikan bahwa

$begin mathsize 14px style limit as straight x rightwards arrow 4 of fraction numerator square root of 4 minus square root of straight x plus 5 end root end root minus square root of square root of straight x plus 5 end root minus 2 end root over denominator 3 minus square root of straight x plus 5 end root end fraction equals limit as straight x rightwards arrow 4 of open parentheses fraction numerator square root of 4 minus square root of straight x plus 5 end root end root minus square root of square root of straight x plus 5 end root minus 2 end root over denominator 3 minus square root of straight x plus 5 end root end fraction times fraction numerator square root of 4 minus square root of straight x plus 5 end root end root plus square root of square root of straight x plus 5 end root minus 2 end root over denominator square root of 4 minus square root of straight x plus 5 end root end root plus square root of square root of straight x plus 5 end root minus 2 end root end fraction close parentheses equals limit as straight x rightwards arrow 4 of fraction numerator open parentheses 4 minus square root of straight x plus 5 end root close parentheses minus open parentheses square root of straight x plus 5 end root minus 2 close parentheses over denominator open parentheses 3 minus square root of straight x plus 5 end root close parentheses open parentheses square root of 4 minus square root of straight x plus 5 end root end root plus square root of square root of straight x plus 5 end root minus 2 end root close parentheses end fraction equals limit as straight x rightwards arrow 4 of fraction numerator 6 minus 2 square root of straight x plus 5 end root over denominator open parentheses 3 minus square root of straight x plus 5 end root close parentheses open parentheses square root of 4 minus square root of straight x plus 5 end root end root plus square root of square root of straight x plus 5 end root minus 2 end root close parentheses end fraction equals limit as straight x rightwards arrow 4 of fraction numerator 2 open parentheses 3 minus square root of straight x plus 5 end root close parentheses over denominator open parentheses 3 minus square root of straight x plus 5 end root close parentheses open parentheses square root of 4 minus square root of straight x plus 5 end root end root plus square root of square root of straight x plus 5 end root minus 2 end root close parentheses end fraction equals limit as straight x rightwards arrow 4 of fraction numerator 2 over denominator square root of 4 minus square root of straight x plus 5 end root end root plus square root of square root of straight x plus 5 end root minus 2 end root end fraction equals fraction numerator 2 over denominator square root of 4 minus square root of 4 plus 5 end root end root plus square root of square root of 4 plus 5 end root minus 2 end root end fraction equals fraction numerator 2 over denominator square root of 4 minus square root of 9 end root plus square root of square root of 9 minus 2 end root end fraction equals fraction numerator 2 over denominator square root of 4 minus 3 end root plus square root of 3 minus 2 end root end fraction equals fraction numerator 2 over denominator square root of 1 plus square root of 1 end fraction equals fraction numerator 2 over denominator 1 plus 1 end fraction equals 2 over 2 equals 1 end style$

Jadi, jawaban yang tepat adalah C.