Tentukan nilai dari x→1lim​x2−13x−2​!

Pertanyaan

Tentukan nilai dari begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 3 x minus 2 over denominator x squared minus 1 end fraction end style!

S. Solehuzain

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

nilai dari limit tersebut adalah begin mathsize 14px style 3 over 2 space atau space 1 end style.

Pembahasan

Diketahui begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 3 x minus 2 over denominator x squared minus 1 end fraction end style. Maka:

begin mathsize 14px style limit as x rightwards arrow 1 of equals fraction numerator 3 x minus 2 over denominator x squared minus 1 end fraction equals fraction numerator 3 open parentheses 1 close parentheses minus 2 over denominator 1 squared minus 1 end fraction equals fraction numerator 3 minus 2 over denominator 1 minus 1 end fraction equals 1 over 0 end style 

Dengan bentuk yang demikian, limit tersebut tidak dapat diselesaikan. Sehingga harus ada perubahan dari soal, yaitu:

begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 3 x minus 3 over denominator x squared minus 1 end fraction equals limit as x rightwards arrow 1 of fraction numerator 3 open parentheses x minus 1 close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses end fraction limit as x rightwards arrow 1 of fraction numerator 3 x minus 3 over denominator x squared minus 1 end fraction equals limit as x rightwards arrow 1 of fraction numerator 3 over denominator open parentheses x plus 1 close parentheses end fraction limit as x rightwards arrow 1 of fraction numerator 3 x minus 3 over denominator x squared minus 1 end fraction equals fraction numerator 3 over denominator open parentheses 1 plus 1 close parentheses end fraction limit as x rightwards arrow 1 of fraction numerator 3 x minus 3 over denominator x squared minus 1 end fraction equals 3 over 2 end style 

atau

 begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator 2 x minus 2 over denominator x squared minus 1 end fraction equals limit as x rightwards arrow 1 of fraction numerator 2 open parentheses x minus 1 close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses end fraction limit as x rightwards arrow 1 of fraction numerator 3 x minus 3 over denominator x squared minus 1 end fraction equals limit as x rightwards arrow 1 of fraction numerator 2 over denominator open parentheses x plus 1 close parentheses end fraction limit as x rightwards arrow 1 of fraction numerator 3 x minus 3 over denominator x squared minus 1 end fraction equals fraction numerator 2 over denominator 1 plus 1 end fraction limit as x rightwards arrow 1 of fraction numerator 3 x minus 3 over denominator x squared minus 1 end fraction equals 2 over 2 limit as x rightwards arrow 1 of fraction numerator 3 x minus 3 over denominator x squared minus 1 end fraction equals 1 end style 

Dengan demikian, nilai dari limit tersebut adalah begin mathsize 14px style 3 over 2 space atau space 1 end style.

40

5.0 (3 rating)

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