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人気のある微分積分 >

limit as x approaches 0 of (sqrt(2-x)-sqrt(2+x))/x

解

x \to 0 lim (\frac{2 - x - 2 + x}{x})

解

- \frac{1}{2}

+1

十進法表記

- 0.70710 \dots

解答ステップ

x \to 0 lim (\frac{2 - x - 2 + x}{x})

分子を有理化する

\frac{2 - x - 2 + x}{x} : - \frac{2}{- x + 2 + x + 2}

= x \to 0 lim (- \frac{2}{- x + 2 + x + 2})

値を挿入する

x = 0

= - \frac{2}{- 0 + 2 + 0 + 2}

簡素化

= - \frac{1}{2}

グラフ

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