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Pertanyaan

Hitunglah limit fungsi berikut!

begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x to the power of 4 minus 6 x squared over denominator x cubed plus 2 x squared end fraction end style        

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

nilai  begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x to the power of 4 minus 6 x squared over denominator x cubed plus 2 x squared end fraction end styleadalah begin mathsize 14px style negative 3 end style

Pembahasan

begin mathsize 14px style x equals 0 end style disubtitusikan pada limit tersebut

     begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x to the power of 4 minus 6 x squared over denominator x cubed plus 2 x squared end fraction equals fraction numerator 0 minus 6 times 0 over denominator 0 plus 2 times 0 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 0 of fraction numerator x to the power of 4 minus 6 x squared over denominator x cubed plus 2 x squared end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator up diagonal strike x squared end strike left parenthesis x squared minus 6 right parenthesis over denominator up diagonal strike x squared end strike left parenthesis x plus 2 right parenthesis end fraction end cell row cell space space space space space space space space space space space space space space space space end cell equals cell space fraction numerator 0 minus 6 over denominator 0 plus 2 end fraction end cell row cell space space space space space space space space space space space space space space space space end cell equals cell negative 6 over 2 end cell row cell space space space space space space space space space space space space space space space space end cell equals cell negative 3 end cell end table end style     

Jadi, nilai  begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator x to the power of 4 minus 6 x squared over denominator x cubed plus 2 x squared end fraction end styleadalah begin mathsize 14px style negative 3 end style

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