x→10lim​2x−93x−8​=. . .

Pertanyaan

limit as x rightwards arrow 10 of fraction numerator 3 x minus 8 over denominator 2 x minus 9 end fraction equals. . .

  1. negative 1 

  2. negative 8 over 9

  3. 8 over 9

  4. 1 

  5. 2

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Ingat sifat limit 

  • limit as x rightwards arrow a of space k equals k
  • limit as x rightwards arrow a of space x equals a
  • limit as x rightwards arrow a of space k x equals k times 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 fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction close square brackets equals fraction numerator limit as x rightwards arrow a of f left parenthesis x right parenthesis over denominator limit as x rightwards arrow a of g left parenthesis x right parenthesis end fraction

Dengan menggunakan sifat-sifat diatas maka diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 10 of fraction numerator 3 x minus 8 over denominator 2 x minus 9 end fraction end cell equals cell fraction numerator limit as x rightwards arrow 10 of 3 x minus 8 over denominator limit as x rightwards arrow 10 of 2 x minus 9 end fraction end cell row blank equals cell fraction numerator limit as x rightwards arrow 10 of 3 x minus limit as x rightwards arrow 10 of 8 over denominator limit as x rightwards arrow 10 of 2 x minus limit as x rightwards arrow 10 of 9 end fraction end cell row blank equals cell fraction numerator 3 times limit as x rightwards arrow 10 of x minus limit as x rightwards arrow 10 of 8 over denominator 2 times limit as x rightwards arrow 10 of x minus limit as x rightwards arrow 10 of 9 end fraction end cell row blank equals cell fraction numerator left parenthesis 3 times 10 right parenthesis minus 8 over denominator left parenthesis 2 times 10 right parenthesis minus 9 end fraction end cell row blank equals cell fraction numerator 30 minus 8 over denominator 20 minus 9 end fraction end cell row blank equals cell 22 over 11 end cell row blank equals 2 end table

Oleh karena itu, jawaban yang benar adalah E.

95

4.4 (5 rating)

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