Pertanyaan

Tentukan nilai dari x → 1 lim x 2 − 1 3 x − 2 !

Tentukan nilai dari $x \to 1 lim \frac{3 x - 2}{x ^{2} - 1}$ !

S. Solehuzain

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

nilai dari limit tersebut adalah .

nilai dari limit tersebut adalah

Pembahasan

Diketahui . Maka: Dengan bentuk yang demikian, limit tersebut tidak dapat diselesaikan. Sehingga harus ada perubahan dari soal, yaitu: atau Dengan demikian, nilai dari limit tersebut adalah .

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 .