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Jika f(x)=a→0lim​ax+a1​−x1​​ dan f(b)=6−1​ maka b=...

Pertanyaan

Jika f open parentheses x close parentheses equals limit as a rightwards arrow 0 of fraction numerator begin display style fraction numerator 1 over denominator x plus a end fraction end style minus begin display style 1 over x end style over denominator a end fraction dan f open parentheses b close parentheses equals fraction numerator negative 1 over denominator 6 end fraction maka b equals... 

  1. fraction numerator 1 over denominator square root of 6 end fraction atau fraction numerator negative 1 over denominator square root of 6 end fraction 

  2. 1 over 6 atau fraction numerator negative 1 over denominator 6 end fraction 

  3. square root of 6 atau negative square root of 6 

  4. 3 

  5. 6 

Y. Herlanda

Master Teacher

Mahasiswa/Alumni STKIP PGRI Jombang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah C.

Menentukan Nilai Limit Fungsi Aljabar dengan Metode Pemfaktoran

f open parentheses x close parentheses equals limit as a rightwards arrow 0 of fraction numerator begin display style fraction numerator 1 over denominator x plus a end fraction end style minus begin display style 1 over x end style over denominator a end fraction 

Substitusikan nilai a equals 0 ke fungsi di atas, sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell limit as a rightwards arrow 0 of fraction numerator begin display style fraction numerator 1 over denominator x plus a end fraction end style minus begin display style 1 over x end style over denominator a end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 over denominator x plus 0 end fraction minus 1 over x end style over denominator 0 end fraction end cell row blank equals cell 0 over 0 end cell end table 

Karena 0 over 0 merupakan bentuk tak tentu, maka bentuk tersebut disederhanakan menjadi:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell limit as a rightwards arrow 0 of fraction numerator begin display style fraction numerator 1 over denominator x plus a end fraction end style minus begin display style 1 over x end style over denominator a end fraction end cell row blank equals cell limit as a rightwards arrow 0 of fraction numerator begin display style fraction numerator x minus x plus a over denominator x open parentheses x plus a close parentheses end fraction end style over denominator a end fraction end cell row blank equals cell limit as a rightwards arrow 0 of fraction numerator begin display style fraction numerator a over denominator x open parentheses x plus a close parentheses end fraction end style over denominator a end fraction end cell row blank equals cell limit as a rightwards arrow 0 of fraction numerator up diagonal strike a over denominator x open parentheses x plus a close parentheses end fraction cross times fraction numerator 1 over denominator up diagonal strike a end fraction end cell row blank equals cell limit as a rightwards arrow 0 of fraction numerator 1 over denominator x open parentheses x plus a close parentheses end fraction end cell end table 

Jika f open parentheses b close parentheses equals fraction numerator negative 1 over denominator 6 end fraction maka b equals... 

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses b close parentheses end cell equals cell limit as a rightwards arrow 0 of fraction numerator 1 over denominator x open parentheses x plus a close parentheses end fraction end cell row cell fraction numerator negative 1 over denominator 6 end fraction end cell equals cell fraction numerator 1 over denominator x open parentheses x plus 0 close parentheses end fraction end cell row cell fraction numerator negative 1 over denominator 6 end fraction end cell equals cell 1 over x squared end cell row cell negative x squared end cell equals 6 row cell x squared end cell equals cell negative 6 end cell row cell x squared end cell equals cell 6 i end cell row x equals cell plus-or-minus square root of 6 i end root end cell row cell x subscript 1 end cell equals cell square root of 6 i end root end cell row blank blank atau row cell x subscript 2 end cell equals cell negative square root of 6 i end root end cell end table 

Penyelesaian dalam bentuk imajiner, sehingga tidak ada pilihan jawaban yang tepat.

Jika f open parentheses b close parentheses equals 1 over 6, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses b close parentheses end cell equals cell limit as a rightwards arrow 0 of fraction numerator 1 over denominator x open parentheses x plus a close parentheses end fraction end cell row cell 1 over 6 end cell equals cell fraction numerator 1 over denominator x open parentheses x plus 0 close parentheses end fraction end cell row cell 1 over 6 end cell equals cell 1 over x squared end cell row cell x squared end cell equals 6 row x equals cell plus-or-minus square root of 6 end cell row cell x subscript 1 end cell equals cell square root of 6 end cell row blank blank atau row cell x subscript 2 end cell equals cell negative square root of 6 end cell end table 

Dengan demikian, diperoleh nilai b yaitu square root of 6 atau negative square root of 6.

Oleh karena itu, jawaban yang benar adalah C.

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