Pertanyaan

Hasil dari x → 1 lim x + 4 − 6 − x 3 x 2 + 2 x − 5 adalah....

Hasil dari $x \to 1 lim \frac{3 x ^{2} + 2 x - 5}{x + 4 - 6 - x}$ adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi maka didapatkan hasil sehingga perlu dicari cara lain untuk mencari nilai limitnya. Perhatikan perhitungan berikut! Jadi, jawaban yang tepat adalah C.

Perhatikan bahwa jika dilakukan substitusi x equals 1 comma maka didapatkan hasil 0 over 0 sehingga perlu dicari cara lain untuk mencari nilai limitnya.

Perhatikan perhitungan berikut!

$limit as x rightwards arrow 1 of fraction numerator 3 x squared plus 2 x minus 5 over denominator square root of x plus 4 end root minus square root of 6 minus x end root end fraction equals limit as x rightwards arrow 1 of open parentheses fraction numerator 3 x squared plus 2 x minus 5 over denominator square root of x plus 4 end root minus square root of 6 minus x end root end fraction times fraction numerator square root of x plus 4 end root plus square root of 6 minus x end root over denominator square root of x plus 4 end root plus square root of 6 minus x end root end fraction close parentheses equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator open parentheses square root of x plus 4 end root close parentheses squared minus open parentheses square root of 6 minus x end root close parentheses squared end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator open parentheses x plus 4 close parentheses minus open parentheses 6 minus x close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator x plus 4 minus 6 plus x end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator 2 x minus 2 end fraction equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x squared plus 2 x minus 5 close parentheses open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses over denominator 2 open parentheses x minus 1 close parentheses end fraction equals limit as x rightwards arrow 1 of fraction numerator 3 x squared plus 2 x minus 5 over denominator 2 open parentheses x minus 1 close parentheses end fraction times limit as x rightwards arrow 1 of open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses equals limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x plus 5 close parentheses open parentheses x minus 1 close parentheses over denominator 2 open parentheses x minus 1 close parentheses end fraction times limit as x rightwards arrow 1 of open parentheses square root of x plus 4 end root plus square root of 6 minus x end root close parentheses equals open parentheses limit as x rightwards arrow 1 of fraction numerator open parentheses 3 x plus 5 close parentheses open parentheses x minus 1 close parentheses over denominator 2 open parentheses x minus 1 close parentheses end fraction close parentheses times open parentheses square root of 1 plus 4 end root plus square root of 6 minus 1 end root close parentheses equals open parentheses limit as x rightwards arrow 1 of fraction numerator 3 x plus 5 over denominator 2 end fraction close parentheses times open parentheses square root of 5 plus square root of 5 close parentheses equals fraction numerator 3 open parentheses 1 close parentheses plus 5 over denominator 2 end fraction times 2 square root of 5 equals fraction numerator 3 plus 5 over denominator 2 end fraction times 2 square root of 5 equals 8 over 2 times 2 square root of 5 equals 8 over 2 times 2 square root of 5 equals 8 square root of 5$

Jadi, jawaban yang tepat adalah C.