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

F. Freelancer8

Master Teacher

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.