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Pertanyaan

Hitunglah limit fungsi berikut!

begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator x squared minus 25 over denominator x squared minus 4 x minus 5 end fraction end style          

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

nilaibegin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator x squared minus 25 over denominator x squared minus 4 x minus 5 end fraction end style  adalah begin mathsize 14px style 1 2 over 3 end style 

Pembahasan

begin mathsize 14px style x equals 5 end style disubtitusikan pada limit tersebut

     begin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator x squared minus 25 over denominator x squared minus 4 x minus 5 end fraction equals fraction numerator 5 squared minus 25 over denominator 5 squared minus 4 open parentheses 5 close parentheses minus 5 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 5 of fraction numerator x squared minus 25 over denominator x squared minus 4 x minus 5 end fraction end cell equals cell limit as x rightwards arrow 5 of fraction numerator up diagonal strike open parentheses x minus 5 close parentheses end strike open parentheses x plus 5 close parentheses over denominator up diagonal strike open parentheses x minus 5 close parentheses end strike open parentheses x plus 1 close parentheses 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 end cell equals cell fraction numerator 5 plus 5 over denominator 5 plus 1 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 end cell equals cell 10 over 6 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 end cell equals cell 1 2 over 3 end cell end table end style      

Jadi, nilaibegin mathsize 14px style limit as x rightwards arrow 5 of fraction numerator x squared minus 25 over denominator x squared minus 4 x minus 5 end fraction end style  adalah begin mathsize 14px style 1 2 over 3 end style 

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