Pertanyaan

x → 0 lim x x + 1 − 1 − x = ...

$x \to 0 lim \frac{x + 1 - 1 - x}{x} = ...$

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Habis dalam

Klaim

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai adalah 1

nilai $begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of x plus 1 end root minus square root of 1 minus x end root over denominator x end fraction end style$ adalah 1

Pembahasan

disubtitusikan pada limit tersebut Karena menghasilkan limit bentuk tak tentumaka akan ditentukan dengan metode mengalikannya dengan akar sekawan Jadi, nilai adalah 1

begin mathsize 14px style x equals 0 end style disubtitusikan pada limit tersebut

$begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of x plus 1 end root minus square root of 1 minus x end root over denominator x end fraction equals fraction numerator square root of 0 plus 1 end root minus square root of 1 minus 0 end root over denominator 0 end fraction equals 0 over 0 end style$

Karena menghasilkan limit bentuk tak tentu maka akan ditentukan dengan metode mengalikannya dengan akar sekawan

$begin mathsize 14px style space space space space space limit as x rightwards arrow 0 of fraction numerator square root of x plus 1 end root minus square root of 1 minus x end root over denominator x end fraction times fraction numerator square root of x plus 1 end root plus square root of 1 minus x end root over denominator square root of x plus 1 end root plus square root of 1 minus x end root end fraction stack left right double arrow lim with x rightwards arrow 0 below fraction numerator open parentheses x plus 1 close parentheses minus open parentheses 1 minus x close parentheses over denominator x open parentheses square root of x plus 1 end root plus square root of 1 minus x end root close parentheses end fraction left right double arrow limit as x rightwards arrow 0 of fraction numerator x plus 1 minus 1 plus x over denominator x left parenthesis square root of x plus 1 end root plus square root of 1 minus x end root right parenthesis end fraction left right double arrow limit as x rightwards arrow 0 of fraction numerator 2 up diagonal strike x over denominator up diagonal strike x left parenthesis square root of x plus 1 end root plus square root of 1 minus x end root right parenthesis end fraction left right double arrow limit as x rightwards arrow 0 of fraction numerator 2 over denominator square root of x plus 1 end root plus square root of 1 minus x end root end fraction left right double arrow space fraction numerator 2 over denominator square root of 0 plus 1 end root plus square root of 1 minus 0 end root end fraction left right double arrow fraction numerator 2 over denominator 1 plus 1 end fraction equals 1 end style$

Jadi, nilai $begin mathsize 14px style limit as x rightwards arrow 0 of fraction numerator square root of x plus 1 end root minus square root of 1 minus x end root over denominator x end fraction end style$ adalah 1