Pertanyaan

x → 4 lim 13 − x − x + 5 16 − x 2 = ....

$x \to 4 lim \frac{16 - x ^{2}}{13 - x - x + 5} =$ ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa

$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 16 minus straight x squared over denominator square root of 13 minus straight x end root minus square root of straight x plus 5 end root end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application fraction numerator open parentheses 4 plus straight x close parentheses open parentheses 4 minus straight x close parentheses over denominator square root of 13 minus straight x end root minus square root of straight x plus 5 end root end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application open parentheses fraction numerator open parentheses 4 plus straight x close parentheses open parentheses 4 minus straight x close parentheses over denominator square root of 13 minus straight x end root minus square root of straight x plus 5 end root end fraction times fraction numerator square root of 13 minus straight x end root plus square root of straight x plus 5 end root over denominator square root of 13 minus straight x end root plus square root of straight x plus 5 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 open parentheses 4 plus straight x close parentheses open parentheses 4 minus straight x close parentheses open parentheses square root of 13 minus straight x end root plus square root of straight x plus 5 end root close parentheses over denominator open parentheses 13 minus straight x close parentheses minus open parentheses straight x plus 5 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 4 plus straight x close parentheses open parentheses 4 minus straight x close parentheses open parentheses square root of 13 minus straight x end root plus square root of straight x plus 5 end root close parentheses over denominator 8 minus 2 straight x end fraction end cell row blank equals cell limit as straight x rightwards arrow 4 of invisible function application fraction numerator open parentheses 4 plus straight x close parentheses open parentheses 4 minus straight x close parentheses open parentheses square root of 13 minus straight x end root plus square root of straight x plus 5 end root close parentheses over denominator 2 open parentheses 4 minus straight x 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 4 plus straight x close parentheses open parentheses square root of 13 minus straight x end root plus square root of straight x plus 5 end root close parentheses over denominator 2 end fraction end cell row blank equals cell fraction numerator open parentheses 4 plus 4 close parentheses open parentheses square root of 13 minus 4 end root plus square root of 4 plus 5 end root close parentheses over denominator 2 end fraction end cell row blank equals cell fraction numerator open parentheses 8 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 4 open parentheses 3 plus 3 close parentheses end cell row blank equals cell 4 open parentheses 6 close parentheses end cell row blank equals 24 end table end style$

Jadi, jawaban yang tepat adalah D.