Pertanyaan

x → 0 lim 2 x 1 + x − 1 − x = ...

$x \to 0 lim \frac{1 + x - 1 - x}{2 x} = ...$

$\frac{1}{2}$
$\frac{1}{3}$
$\frac{1}{2} 2$
$\frac{1}{2} 3$
$\frac{1}{3} 2$

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$begin mathsize 12px style limit as x rightwards arrow 0 of fraction numerator blank square root of 1 plus square root of x end root minus square root of 1 minus square root of x end root over denominator square root of 2 x end root end fraction equals limit as x rightwards arrow 0 of fraction numerator blank square root of 1 plus square root of x end root minus square root of 1 minus square root of x end root over denominator square root of 2 x end root end fraction cross times fraction numerator square root of 1 plus square root of x end root plus square root of 1 minus square root of x end root over denominator square root of 1 plus square root of x end root plus square root of 1 minus square root of x end root end fraction equals limit as x rightwards arrow 0 of fraction numerator blank 1 over denominator square root of 2 x end root end fraction cross times fraction numerator open parentheses 1 plus square root of x close parentheses minus open parentheses 1 minus square root of x close parentheses over denominator square root of 1 plus square root of x end root plus square root of 1 minus square root of x end root end fraction equals limit as x rightwards arrow 0 of space fraction numerator blank 1 over denominator square root of 2 blank up diagonal strike square root of x end strike end fraction cross times fraction numerator 2 up diagonal strike square root of x end strike over denominator square root of 1 plus square root of x end root plus square root of 1 minus square root of x end root end fraction equals fraction numerator blank 1 over denominator square root of 2 blank end fraction cross times fraction numerator 2 over denominator square root of 1 plus square root of 0 end root plus square root of 1 minus square root of 0 end root end fraction equals fraction numerator blank 1 over denominator square root of 2 blank end fraction cross times 2 over 2 equals fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals 1 half square root of 2 end style$