x→7lim​x−749−x2​= ...

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow 7 of fraction numerator 49 minus x squared over denominator x minus 7 end fraction equals space... end style  

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style limit as x rightwards arrow 7 of fraction numerator 49 minus x squared over denominator x minus 7 end fraction end style adalah begin mathsize 14px style negative 14 end style.

Pembahasan

begin mathsize 14px style x equals 7 end style disubtitusikan pada limit tersebut

begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 49 minus x squared over denominator x minus 7 end fraction equals fraction numerator 49 minus 7 squared over denominator x minus 7 end fraction equals 0 over 0 end style 

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

begin mathsize 14px style limit as x rightwards arrow 7 of fraction numerator 49 minus x squared over denominator x minus 7 end fraction equals limit as x rightwards arrow x of fraction numerator up diagonal strike open parentheses 7 minus x close parentheses end strike open parentheses 7 plus x close parentheses over denominator negative up diagonal strike open parentheses 7 minus x close parentheses end strike end fraction space space space space space space space space space space space space space space space space space space equals fraction numerator 7 plus 7 over denominator negative 1 end fraction space space space space space space space space space space space space space space space space space space equals negative 14 end style  

Jadi, nilai begin mathsize 14px style limit as x rightwards arrow 7 of fraction numerator 49 minus x squared over denominator x minus 7 end fraction end style adalah begin mathsize 14px style negative 14 end style.

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