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Pertanyaan

Tentukan nilai limit dari fungsi-fungsi berikut ini:

begin mathsize 14px style limit as x rightwards arrow 16 of fraction numerator x minus 16 over denominator square root of x minus 4 end fraction end style 

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

nilai dari begin mathsize 14px style limit as x rightwards arrow 16 of fraction numerator x minus 16 over denominator square root of x minus 4 end fraction end style adalah begin mathsize 14px style 8 end style

Pembahasan

Perhatikan perhitungan berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 16 of fraction numerator x minus 16 over denominator square root of x minus 4 end fraction end cell equals cell fraction numerator 16 minus 16 over denominator square root of 16 minus 4 end fraction end cell row blank equals cell fraction numerator 16 minus 16 over denominator 4 minus 4 end fraction end cell row blank equals cell 0 over 0 end cell end table  

Karena hasil dari limit tersebut ketika disubstitusikan x equals 16 merupakan bilangan tak tentu 0 over 0, maka kita lakukan pemfaktoran pada bentuk limit tersebut.

Ingat:

begin mathsize 14px style a squared minus b squared equals open parentheses a plus b close parentheses open parentheses a minus b close parentheses end style 

Dengan menggunakan metode pemfaktoran, maka didapatkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 16 of fraction numerator x minus 16 over denominator square root of x minus 4 end fraction end cell equals cell limit as x rightwards arrow 16 of fraction numerator open parentheses square root of x plus 4 close parentheses down diagonal strike open parentheses square root of x minus 4 close parentheses end strike over denominator down diagonal strike square root of x minus 4 end strike end fraction end cell row blank equals cell limit as x rightwards arrow 16 of square root of x plus 4 end cell row blank equals cell square root of 16 plus 4 end cell row blank equals cell 4 plus 4 end cell row blank equals 8 end table end style 

Jadi, nilai dari begin mathsize 14px style limit as x rightwards arrow 16 of fraction numerator x minus 16 over denominator square root of x minus 4 end fraction end style adalah begin mathsize 14px style 8 end style

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