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Hitunglah limit fungsi berikut! b. x → 2 1 ​ lim ​ 2 x − 1 12 x 2 − 3 ​

Hitunglah limit fungsi berikut!

b.    

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A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

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Jawaban

nilai adalah 6.

nilai begin mathsize 14px style limit as x rightwards arrow 1 half of fraction numerator 12 x squared minus 3 over denominator 2 x minus 1 end fraction end style adalah 6.

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Pembahasan

Pertama, disubtitusikan pada limit tersebut Karena menghasilkan limit bentuk tak tentu, maka akan ditentukan dengan metode pemfaktoran Jadi, nilai adalah 6.

Pertama, begin mathsize 14px style x equals 1 half end style disubtitusikan pada limit tersebut

   begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 half of fraction numerator 12 x squared minus 3 over denominator 2 x minus 1 end fraction end cell equals cell fraction numerator 12 open parentheses begin display style 1 half end style close parentheses squared minus 3 over denominator 2 open parentheses begin display style 1 half end style close parentheses minus 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 end cell equals cell fraction numerator 12 times begin display style 1 fourth end style minus 3 over denominator 1 minus 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 end cell equals cell 0 over 0 end cell end table 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 1 half of fraction numerator 12 x squared minus 3 over denominator 2 x minus 1 end fraction end cell equals cell fraction numerator 3 open parentheses 4 x squared minus 1 close parentheses over denominator 2 x equals 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 end cell equals cell fraction numerator 3 up diagonal strike open parentheses 2 x equals 1 close parentheses end strike open parentheses 2 x plus 1 close parentheses over denominator up diagonal strike open parentheses 2 x minus 1 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 end cell equals cell 3 times open parentheses 2 open parentheses 1 half close parentheses plus 1 close parentheses end cell row cell space space space space space space space space space space space space space space space space space space space space end cell equals cell 3 times 2 end cell row cell space space space space space space space space space space space space space space space space space space space space end cell equals 6 end table end style 

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 1 half of fraction numerator 12 x squared minus 3 over denominator 2 x minus 1 end fraction end style adalah 6.

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