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x→2lim​ 12x+15x−1​​=. . .

Pertanyaan

limit as x rightwards arrow 2 of space square root of fraction numerator 5 x minus 1 over denominator 12 x plus 1 end fraction end root equals. . .

  1. 0 comma 2 

  2. 0 comma 3

  3. 0 comma 4 

  4. 0 comma 5 

  5. 0 comma 6 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah E.

Ingat sifat limit 

  • limit as x rightwards arrow a of space x equals a
  • limit as x rightwards arrow a of space k equals k
  • limit as x rightwards arrow a of space k x equals k. limit as x rightwards arrow a of x
  • limit as x rightwards arrow a of space open square brackets f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis close square brackets equals limit as x rightwards arrow a of f left parenthesis x right parenthesis minus limit as x rightwards arrow a of g left parenthesis x right parenthesis
  • limit as x rightwards arrow a of space open square brackets f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis close square brackets equals limit as x rightwards arrow a of f left parenthesis x right parenthesis plus limit as x rightwards arrow a of g left parenthesis x right parenthesis
  • limit as x rightwards arrow a of space open square brackets f left parenthesis x right parenthesis divided by g left parenthesis x right parenthesis close square brackets equals limit as x rightwards arrow a of f left parenthesis x right parenthesis divided by limit as x rightwards arrow a of g left parenthesis x right parenthesis
  • limit as x rightwards arrow a of space open square brackets f left parenthesis x right parenthesis close square brackets to the power of n equals open square brackets limit as x rightwards arrow a of f left parenthesis x right parenthesis close square brackets to the power of n

Dengan menggunakan sifat-sifat di atas maka diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 2 of space square root of fraction numerator 5 x minus 1 over denominator 12 x plus 1 end fraction end root end cell equals cell square root of limit as x rightwards arrow 2 of fraction numerator 5 x minus 1 over denominator 12 x plus 1 end fraction end root end cell row blank equals cell square root of fraction numerator limit as x rightwards arrow 2 of left parenthesis 5 x minus 1 right parenthesis over denominator limit as x rightwards arrow 2 of left parenthesis 12 x plus 1 right parenthesis end fraction end root end cell row blank equals cell square root of fraction numerator limit as x rightwards arrow 2 of 5 x minus limit as x rightwards arrow 2 of 1 over denominator limit as x rightwards arrow 2 of 12 x plus limit as x rightwards arrow 2 of 1 end fraction end root end cell row blank equals cell square root of fraction numerator 5 times limit as x rightwards arrow 2 of x minus limit as x rightwards arrow 2 of 1 over denominator 12 times stack lim space x with x rightwards arrow 2 below plus limit as x rightwards arrow 2 of 1 end fraction end root end cell row blank equals cell square root of fraction numerator left parenthesis 5 times 2 right parenthesis minus 1 over denominator left parenthesis 12 times 2 right parenthesis plus 1 end fraction end root end cell row blank equals cell square root of fraction numerator 10 minus 1 over denominator 24 plus 1 end fraction end root end cell row blank equals cell square root of 9 over 25 end root end cell row blank equals cell 3 over 5 end cell row blank equals cell 0 comma 6 end cell end table

 

Oleh karena itu, jawaban yang benar adalah E.

82

5.0 (3 rating)

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