....

Pertanyaan

begin mathsize 14px style lim subscript straight x rightwards arrow 3 end subscript fraction numerator 1 minus open parentheses straight x minus 2 close parentheses to the power of 8 over denominator square root of straight x plus 1 end root minus 2 end fraction equals end style ....

  1. begin mathsize 14px style 32 end style

  2. begin mathsize 14px style 16 end style

  3. begin mathsize 14px style negative 8 end style

  4. begin mathsize 14px style negative 16 end style

  5. begin mathsize 14px style negative 32 end style

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi begin mathsize 14px style x equals 3 end style, maka didapatkan hasil undefined.

Oleh karena itu perlu dicari cara lain untuk mencari nilai limitnya.

Perhatikan perhitungan berikut!

 begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow 3 of fraction numerator 1 minus open parentheses straight x minus 2 close parentheses to the power of 8 over denominator square root of straight x plus 1 end root minus 2 end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator open parentheses 1 plus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 minus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses over denominator square root of straight x plus 1 end root minus 2 end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator open parentheses 1 plus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses straight x minus 2 close parentheses squared close parentheses open parentheses 1 minus open parentheses straight x minus 2 close parentheses squared close parentheses over denominator square root of straight x plus 1 end root minus 2 end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator open parentheses 1 plus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses straight x minus 2 close parentheses squared close parentheses open parentheses 1 plus open parentheses straight x minus 2 close parentheses close parentheses open parentheses 1 minus open parentheses straight x minus 2 close parentheses close parentheses over denominator square root of straight x plus 1 end root minus 2 end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator open parentheses 1 plus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses straight x minus 2 close parentheses squared close parentheses open parentheses straight x minus 1 close parentheses open parentheses negative straight x plus 3 close parentheses over denominator square root of straight x plus 1 end root minus 2 end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of open parentheses fraction numerator open parentheses 1 plus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses straight x minus 2 close parentheses squared close parentheses open parentheses straight x minus 1 close parentheses open parentheses negative straight x plus 3 close parentheses over denominator square root of straight x plus 1 end root minus 2 end fraction times fraction numerator square root of straight x plus 1 end root plus 2 over denominator square root of straight x plus 1 end root plus 2 end fraction close parentheses end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator open parentheses 1 plus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses straight x minus 2 close parentheses squared close parentheses open parentheses straight x minus 1 close parentheses open parentheses negative straight x plus 3 close parentheses open parentheses square root of straight x plus 1 end root plus 2 close parentheses over denominator open parentheses straight x plus 1 close parentheses minus 4 end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator open parentheses 1 plus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses straight x minus 2 close parentheses squared close parentheses open parentheses straight x minus 1 close parentheses open parentheses negative straight x plus 3 close parentheses open parentheses square root of straight x plus 1 end root plus 2 close parentheses over denominator straight x minus 3 end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator open parentheses 1 plus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses straight x minus 2 close parentheses squared close parentheses open parentheses straight x minus 1 close parentheses open parentheses negative straight x plus 3 close parentheses open parentheses square root of straight x plus 1 end root plus 2 close parentheses over denominator negative open parentheses negative straight x plus 3 close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 3 of fraction numerator open parentheses 1 plus open parentheses straight x minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses straight x minus 2 close parentheses squared close parentheses open parentheses straight x minus 1 close parentheses open parentheses square root of straight x plus 1 end root plus 2 close parentheses over denominator negative 1 end fraction end cell row blank equals cell fraction numerator open parentheses 1 plus open parentheses 3 minus 2 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses 3 minus 2 close parentheses squared close parentheses open parentheses 3 minus 1 close parentheses open parentheses square root of 3 plus 1 end root plus 2 close parentheses over denominator negative 1 end fraction end cell row blank equals cell fraction numerator open parentheses 1 plus open parentheses 1 close parentheses to the power of 4 close parentheses open parentheses 1 plus open parentheses 1 close parentheses squared close parentheses open parentheses 2 close parentheses open parentheses square root of 4 plus 2 close parentheses over denominator negative 1 end fraction end cell row blank equals cell fraction numerator open parentheses 1 plus 1 close parentheses open parentheses 1 plus 1 close parentheses open parentheses 2 close parentheses open parentheses 2 plus 2 close parentheses over denominator negative 1 end fraction end cell row blank equals cell fraction numerator open parentheses 2 close parentheses open parentheses 2 close parentheses open parentheses 2 close parentheses open parentheses 4 close parentheses over denominator negative 1 end fraction end cell row blank equals cell negative 32 end cell end table end style

Jadi, jawaban yang tepat adalah E.

57

5.0 (2 rating)

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