Pertanyaan

x → 1 lim x − 1 x − 2 x − 1

$x \to 1 lim \frac{x - 2 x - 1}{x - 1}$

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Habis dalam

Klaim

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

hasil dari adalah .

hasil dari $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x minus square root of 2 x minus 1 end root over denominator x minus 1 end fraction end style$ adalah begin mathsize 14px style negative 1 half end style

begin mathsize 14px style negative 1 half end style

Pembahasan

Mencari hasil dari limit tersebut: Jadi, hasil dari adalah .

Mencari hasil dari limit tersebut:

$begin mathsize 14px style limit as x rightwards arrow thin space 1 of open parentheses fraction numerator square root of x minus square root of 2 x minus 1 end root over denominator x minus 1 end fraction close parentheses equals limit as x rightwards arrow thin space 1 of open parentheses fraction numerator square root of x minus square root of 2 x minus 1 end root over denominator x minus 1 end fraction times fraction numerator begin display style fraction numerator square root of x plus square root of 2 x minus 1 end root over denominator square root of x plus square root of 2 x minus 1 end root end fraction end style over denominator 1 end fraction close parentheses equals limit as x rightwards arrow thin space 1 of open parentheses fraction numerator fraction numerator negative x plus 1 over denominator square root of x plus square root of 2 x minus 1 end root end fraction over denominator x minus 1 end fraction close parentheses equals limit as x rightwards arrow thin space 1 of open parentheses fraction numerator 1 over denominator x minus 1 end fraction times fraction numerator negative x plus 1 over denominator square root of x plus square root of 2 x minus 1 end root end fraction close parentheses equals limit as x rightwards arrow thin space 1 of open parentheses fraction numerator 1 over denominator negative left parenthesis negative x plus 1 right parenthesis end fraction times fraction numerator negative x plus 1 over denominator square root of x plus square root of 2 x minus 1 end root end fraction close parentheses equals limit as x rightwards arrow thin space 1 of open parentheses negative fraction numerator 1 over denominator square root of x plus square root of 2 x minus 1 end root end fraction close parentheses equals negative fraction numerator 1 over denominator square root of 1 plus square root of 2 times thin space 1 minus 1 end root end fraction equals negative fraction numerator 1 over denominator 1 plus square root of 1 end fraction equals negative fraction numerator 1 over denominator 1 plus 1 end fraction equals negative 1 half end style$

Jadi, hasil dari $begin mathsize 14px style limit as x rightwards arrow 1 of fraction numerator square root of x minus square root of 2 x minus 1 end root over denominator x minus 1 end fraction end style$ adalah begin mathsize 14px style negative 1 half end style .