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x→8lim​3x​−2x−8​ = ....

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 8 of fraction numerator x minus 8 over denominator cube root of x minus 2 end fraction end style = ....

  1. 8space 

  2. 12space 

  3. 16space 

  4. 20space 

  5. 48space 

S. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Ingat bahwa:

limit as x rightwards arrow c of 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 c of f left parenthesis x right parenthesis over denominator limit as x rightwards arrow c of g left parenthesis x right parenthesis end fraction

Sehingga diperoleh

limit as x rightwards arrow 8 of fraction numerator x minus 8 over denominator cube root of x minus 2 end fraction equals fraction numerator limit as x rightwards arrow 8 of open parentheses x minus 8 close parentheses over denominator limit as x rightwards arrow 8 of open parentheses cube root of x minus 2 close parentheses end fraction

Dengan menggunakan konsep turunan maka

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell x minus 8 end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals 1 row cell g left parenthesis x right parenthesis end cell equals cell cube root of x minus 2 end cell row blank equals cell x to the power of 1 third end exponent minus 2 end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 1 third x to the power of negative 2 over 3 end exponent end cell row blank equals cell fraction numerator 1 over denominator 3 cube root of x squared end root end fraction end cell end table

Maka diperoleh nilai limitnya adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 8 of fraction numerator x minus 8 over denominator cube root of x minus 2 end fraction end cell equals cell fraction numerator limit as x rightwards arrow 8 of space 1 over denominator limit as x rightwards arrow 8 of space begin display style fraction numerator 1 over denominator 3 cube root of x squared end root end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator 3 cube root of 8 squared end root end fraction end style end fraction end cell row blank equals cell 3 cube root of 64 end cell row blank equals cell 3 open parentheses 4 close parentheses end cell row blank equals 12 end table

Oleh karena itu, jawaban yang tepat adalah B.

116

5.0 (6 rating)

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