Pertanyaan

lim x → 2 5 − 2 x − x 2 − 3 4 x 2 − 3 x + 6 − 9 x − 2 = ....

$lim_{x \to 2} \frac{4 x ^{2} - 3 x + 6 - 9 x - 2}{5 - 2 x - x ^{2} - 3} =$ ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi x = 2 , 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 = 2, maka didapatkan hasil .
Sehingga perlu dicari cara lain untuk mencari nilai limitnya.

Perhatikan bahwa

$begin mathsize 14px style limit as straight x rightwards arrow 2 of fraction numerator square root of 4 straight x squared minus 3 straight x plus 6 end root minus square root of 9 straight x minus 2 end root over denominator square root of 5 minus 2 straight x end root minus square root of straight x squared minus 3 end root end fraction equals limit as straight x rightwards arrow 2 of open parentheses fraction numerator square root of 4 straight x squared minus 3 straight x plus 6 end root minus square root of 9 straight x minus 2 end root over denominator square root of 5 minus 2 straight x end root minus square root of straight x squared minus 3 end root end fraction times fraction numerator square root of 4 straight x squared minus 3 straight x plus 6 end root plus square root of 9 straight x minus 2 end root over denominator square root of 4 straight x squared minus 3 straight x plus 6 end root plus square root of 9 straight x minus 2 end root end fraction times fraction numerator square root of 5 minus 2 straight x end root plus square root of straight x squared minus 3 end root over denominator square root of 5 minus 2 straight x end root plus square root of straight x squared minus 3 end root end fraction close parentheses equals limit as straight x rightwards arrow 2 of fraction numerator open parentheses open parentheses 4 straight x squared minus 3 straight x plus 6 close parentheses minus open parentheses 9 straight x minus 2 close parentheses close parentheses open parentheses square root of 5 minus 2 straight x end root plus square root of straight x squared minus 3 end root close parentheses over denominator open parentheses open parentheses 5 minus 2 straight x close parentheses minus open parentheses straight x squared minus 3 close parentheses close parentheses open parentheses square root of 4 straight x squared minus 3 straight x plus 6 end root plus square root of 9 straight x minus 2 end root close parentheses end fraction equals limit as straight x rightwards arrow 2 of fraction numerator open parentheses 4 straight x squared minus 3 straight x plus 6 minus 9 straight x plus 2 close parentheses open parentheses square root of 5 minus 2 straight x end root plus square root of straight x squared minus 3 end root close parentheses over denominator open parentheses 5 minus 2 straight x minus straight x squared plus 3 close parentheses open parentheses square root of 4 straight x squared minus 3 straight x plus 6 end root plus square root of 9 straight x minus 2 end root close parentheses end fraction equals limit as straight x rightwards arrow 2 of fraction numerator open parentheses 4 straight x squared minus 12 straight x plus 8 close parentheses open parentheses square root of 5 minus 2 straight x end root plus square root of straight x squared minus 3 end root close parentheses over denominator open parentheses negative straight x squared minus 2 straight x plus 8 close parentheses open parentheses square root of 4 straight x squared minus 3 straight x plus 6 end root plus square root of 9 straight x minus 2 end root close parentheses end fraction equals limit as straight x rightwards arrow 2 of fraction numerator 4 straight x squared minus 12 straight x plus 8 over denominator negative straight x squared minus 2 straight x plus 8 end fraction times limit as straight x rightwards arrow 2 of fraction numerator square root of 5 minus 2 straight x end root plus square root of straight x squared minus 3 end root over denominator square root of 4 straight x squared minus 3 straight x plus 6 end root plus square root of 9 straight x minus 2 end root end fraction equals limit as straight x rightwards arrow 2 of fraction numerator 4 open parentheses straight x squared minus 3 straight x plus 2 close parentheses over denominator negative open parentheses straight x squared plus 2 straight x minus 8 close parentheses end fraction times fraction numerator square root of 5 minus 2 open parentheses 2 close parentheses end root plus square root of open parentheses 2 close parentheses squared minus 3 end root over denominator square root of 4 open parentheses 2 close parentheses squared minus 3 open parentheses 2 close parentheses plus 6 end root plus square root of 9 open parentheses 2 close parentheses minus 2 end root end fraction equals limit as straight x rightwards arrow 2 of fraction numerator 4 open parentheses straight x minus 1 close parentheses open parentheses straight x minus 2 close parentheses over denominator negative open parentheses straight x plus 4 close parentheses open parentheses straight x minus 2 close parentheses end fraction times fraction numerator square root of 1 plus square root of 1 over denominator square root of 16 plus square root of 16 end fraction equals limit as straight x rightwards arrow 2 of fraction numerator 4 open parentheses straight x minus 1 close parentheses over denominator negative open parentheses straight x plus 4 close parentheses end fraction times fraction numerator 1 plus 1 over denominator 4 plus 4 end fraction equals fraction numerator 4 open parentheses 2 minus 1 close parentheses over denominator negative open parentheses 2 plus 4 close parentheses end fraction times 2 over 8 equals fraction numerator 4 open parentheses 1 close parentheses over denominator negative open parentheses 6 close parentheses end fraction times 2 over 8 equals negative 8 over 48 equals negative 1 over 6 end style$

Jadi, jawaban yang tepat adalah C.