x→64lim​x31​−4x−64​= ...

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 64 of fraction numerator x minus 64 over denominator x to the power of 1 third end exponent minus 4 end fraction equals space... end style 

  1. begin mathsize 14px style 64 end style 

  2. begin mathsize 14px style 56 end style 

  3. begin mathsize 14px style 48 end style 

  4. begin mathsize 14px style 36 end style 

  5. begin mathsize 14px style 24 end style 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Diketahui limit limit as x rightwards arrow 64 of fraction numerator x minus 64 over denominator x to the power of 1 third end exponent minus 4 end fraction maka

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 64 of fraction numerator x minus 64 over denominator x to the power of 1 third end exponent minus 4 end fraction end cell equals cell space fraction numerator 64 minus 64 over denominator open parentheses 64 close parentheses to the power of begin display style 1 third end style end exponent minus 4 end fraction end cell row blank equals cell fraction numerator 0 over denominator left parenthesis 4 cubed right parenthesis to the power of begin display style 1 third end style end exponent minus 4 end fraction end cell row blank equals cell fraction numerator 0 over denominator 4 to the power of 3 cross times begin display style 1 third end style end exponent minus 4 end fraction end cell row blank equals cell fraction numerator 0 over denominator 4 to the power of 1 minus 4 end fraction end cell row blank equals cell fraction numerator 0 over denominator 4 minus 4 end fraction end cell row blank equals cell 0 over 0 end cell end table

Karena hasilnya 0 over 0 maka cara untuk menentukan hasil limit tersebut adalah dengan dikalikan sekawan sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 64 of fraction numerator x minus 64 over denominator x to the power of 1 third end exponent minus 4 end fraction end cell equals cell limit as x rightwards arrow 64 of fraction numerator x minus 64 over denominator cube root of x minus 4 end fraction cross times open parentheses cube root of x plus 4 close parentheses squared over open parentheses cube root of x plus 4 close parentheses squared end cell row blank equals cell limit as x rightwards arrow 64 of fraction numerator up diagonal strike open parentheses x minus 64 close parentheses end strike open parentheses cube root of x plus 4 close parentheses squared over denominator up diagonal strike x minus 64 end strike end fraction end cell row blank equals cell limit as x rightwards arrow 64 of open parentheses cube root of x plus 4 close parentheses squared end cell row blank equals cell open parentheses cube root of 64 plus 4 close parentheses squared end cell row blank equals cell 8 squared end cell row blank equals 64 end table end style     

Sehingga, nilai dari begin mathsize 14px style limit as x rightwards arrow 64 of fraction numerator x minus 64 over denominator x to the power of 1 third end exponent minus 4 end fraction end style adalah begin mathsize 14px style 64 end style

Oleh karena itu, jawaban yang tepat adalah A.

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