Hitunglah limit fungsi berikut! c. x→1lim​x−1x​−1​

Pertanyaan

Hitunglah limit fungsi berikut!

c. begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x minus 1 over denominator x minus 1 end fraction end style

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x minus 1 over denominator x minus 1 end fraction end style adalah begin mathsize 14px style 1 half end style.

Pembahasan

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

   begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x minus 1 over denominator x minus 1 end fraction equals fraction numerator square root of 1 minus 1 over denominator 1 minus 1 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 1 of fraction numerator square root of x minus 1 over denominator x minus 1 end fraction end cell equals cell fraction numerator up diagonal strike open parentheses square root of x minus 1 close parentheses end strike over denominator up diagonal strike open parentheses square root of x minus 1 close parentheses end strike open parentheses square root of 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 end cell equals cell fraction numerator 1 over denominator square root of 1 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 end cell equals cell 1 half end cell end table end style

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x minus 1 over denominator x minus 1 end fraction end style adalah begin mathsize 14px style 1 half end style.

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