Pertanyaan

Hasil dari x → 4 lim x 2 − 16 x − 3 x − 2 adalah ....

Hasil dari $x \to 4 lim \frac{x - 3 x - 2}{x ^{2} - 16}$ adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan perhitungan berikut! Dengan demikian, hasil dari adalah . Jadi, jawaban yang tepat adalah B.

Perhatikan perhitungan berikut!

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 4 of invisible function application fraction numerator square root of straight x minus square root of 3 square root of straight x minus 2 end root over denominator straight x squared minus 16 end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application fraction numerator square root of straight x minus square root of 3 square root of straight x minus 2 end root over denominator open parentheses straight x plus 4 close parentheses open parentheses straight x minus 4 close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application open parentheses fraction numerator square root of straight x minus square root of 3 square root of straight x minus 2 end root over denominator open parentheses straight x plus 4 close parentheses open parentheses straight x minus 4 close parentheses end fraction times fraction numerator square root of straight x plus square root of 3 square root of straight x minus 2 end root over denominator square root of straight x plus square root of 3 square root of straight x minus 2 end root end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application fraction numerator straight x minus open parentheses 3 square root of straight x minus 2 close parentheses over denominator open parentheses straight x plus 4 close parentheses open parentheses straight x minus 4 close parentheses open parentheses square root of straight x plus square root of 3 square root of straight x minus 2 end root close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application fraction numerator straight x minus 3 square root of straight x plus 2 over denominator open parentheses straight x plus 4 close parentheses open parentheses straight x minus 4 close parentheses open parentheses square root of straight x plus square root of 3 square root of straight x minus 2 end root close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application fraction numerator open parentheses square root of straight x close parentheses squared minus 3 square root of straight x plus 2 over denominator open parentheses straight x plus 4 close parentheses open parentheses open parentheses square root of straight x close parentheses squared minus 2 squared close parentheses open parentheses square root of straight x plus square root of 3 square root of straight x minus 2 end root close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application fraction numerator open parentheses square root of straight x minus 1 close parentheses open parentheses square root of straight x minus 2 close parentheses over denominator open parentheses straight x plus 4 close parentheses open parentheses square root of straight x plus 2 close parentheses open parentheses square root of straight x minus 2 close parentheses open parentheses square root of straight x plus square root of 3 square root of straight x minus 2 end root close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application fraction numerator open parentheses square root of straight x minus 1 close parentheses over denominator open parentheses straight x plus 4 close parentheses open parentheses square root of straight x plus 2 close parentheses open parentheses square root of straight x plus square root of 3 square root of straight x minus 2 end root close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses square root of 4 minus 1 close parentheses over denominator open parentheses 4 plus 4 close parentheses open parentheses square root of 4 plus 2 close parentheses open parentheses square root of 4 plus square root of 3 square root of 4 minus 2 end root close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 2 minus 1 close parentheses over denominator open parentheses 4 plus 4 close parentheses open parentheses 2 plus 2 close parentheses open parentheses 2 plus square root of 3 open parentheses 2 close parentheses minus 2 end root close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator open parentheses 8 close parentheses open parentheses 4 close parentheses open parentheses 2 plus square root of 4 close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator open parentheses 8 close parentheses open parentheses 4 close parentheses open parentheses 2 plus 2 close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator open parentheses 8 close parentheses open parentheses 4 close parentheses open parentheses 4 close parentheses end fraction end cell row blank equals cell 1 over 128 end cell end table end style$

Dengan demikian, hasil dari $begin mathsize 14px style limit as x rightwards arrow 4 of fraction numerator square root of x minus square root of 3 square root of x minus 2 end root over denominator x squared minus 16 end fraction end style$ adalah .

Jadi, jawaban yang tepat adalah B.

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