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x→3lim​2x2−3x−93x2−x−24​= ...

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator 3 x squared minus x minus 24 over denominator 2 x squared minus 3 x minus 9 end fraction equals space... end style    

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator 3 x squared minus x minus 24 over denominator 2 x squared minus 3 x minus 9 end fraction end style adalah begin mathsize 14px style 1 8 over 9 end style 

Pembahasan

begin mathsize 14px style x equals 3 end style disubtitusikan pada limit tersebut

begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator 3 x squared minus x minus 24 over denominator 2 x squared minus 3 x minus 9 end fraction equals fraction numerator 3 open parentheses 3 close parentheses squared minus 3 minus 24 over denominator 2 open parentheses 3 close parentheses squared minus 3 open parentheses 3 close parentheses minus 9 end fraction equals 0 over 0 end style  

Karena menghasilkan limit bentuk tak tentu maka akan ditentukan dengan metode pemfaktoran

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator 3 x squared minus x minus 24 over denominator 2 x squared minus 3 x minus 9 end fraction end cell equals cell fraction numerator open parentheses 3 x plus 8 close parentheses up diagonal strike open parentheses x minus 3 close parentheses end strike over denominator open parentheses 2 x plus 3 close parentheses up diagonal strike open parentheses x minus 3 close parentheses end strike end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell fraction numerator 3 times 3 plus 8 over denominator 2 times 3 plus 3 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell 17 over 9 end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space end cell equals cell 1 8 over 9 end cell end table end style    

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator 3 x squared minus x minus 24 over denominator 2 x squared minus 3 x minus 9 end fraction end style adalah begin mathsize 14px style 1 8 over 9 end style 

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