Pertanyaan

Nilai dari x → 3 lim 6 + x − 12 − x x 3 − 9 x adalah ....

Nilai dari $x \to 3 lim \frac{x ^{3} - 9 x}{6 + x - 12 - x}$ adalah ....

27
36
54
108
tidak ada

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F. Freelancer8

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa Jadi, jawaban yang tepat adalah C.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 3 of invisible function application fraction numerator x cubed minus 9 x over denominator square root of 6 plus x end root minus square root of 12 minus x end root end fraction end cell row blank equals cell limit as x rightwards arrow 3 of invisible function application open parentheses fraction numerator x cubed minus 9 x over denominator square root of 6 plus x end root minus square root of 12 minus x end root end fraction times fraction numerator square root of 6 plus x end root plus square root of 12 minus x end root over denominator square root of 6 plus x end root plus square root of 12 minus x end root end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 3 of invisible function application fraction numerator open parentheses x cubed minus 9 x close parentheses open parentheses square root of 6 plus x end root plus square root of 12 minus x end root close parentheses over denominator open parentheses 6 plus x close parentheses minus open parentheses 12 minus x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of invisible function application fraction numerator open parentheses x cubed minus 9 x close parentheses open parentheses square root of 6 plus x end root plus square root of 12 minus x end root close parentheses over denominator 2 x minus 6 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of invisible function application fraction numerator x open parentheses x squared minus 9 close parentheses open parentheses square root of 6 plus x end root plus square root of 12 minus x end root close parentheses over denominator 2 open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of invisible function application fraction numerator x open parentheses x plus 3 close parentheses open parentheses x minus 3 close parentheses open parentheses square root of 6 plus x end root plus square root of 12 minus x end root close parentheses over denominator 2 open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 3 of invisible function application fraction numerator x open parentheses x plus 3 close parentheses open parentheses square root of 6 plus x end root plus square root of 12 minus x end root close parentheses over denominator 2 end fraction end cell row blank equals cell fraction numerator 3 open parentheses 3 plus 3 close parentheses open parentheses square root of 6 plus 3 end root plus square root of 12 minus 3 end root close parentheses over denominator 2 end fraction end cell row blank equals cell fraction numerator 3 open parentheses 6 close parentheses open parentheses square root of 9 plus square root of 9 close parentheses over denominator 2 end fraction end cell row blank equals cell fraction numerator 3 open parentheses 6 close parentheses open parentheses 3 plus 3 close parentheses over denominator 2 end fraction end cell row blank equals cell fraction numerator 3 open parentheses 6 close parentheses open parentheses 6 close parentheses over denominator 2 end fraction end cell row blank equals cell 108 over 2 end cell row blank equals 54 end table end style$

Jadi, jawaban yang tepat adalah C.