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人気のある微分積分 >

limit as z approaches 2 of ((2z-z^2)/(z^2-4))^3

解

z \to 2 lim ((\frac{2 z - z ^{2}}{z ^{2} - 4})^{3})

解

- \frac{1}{8}

+1

十進法表記

- 0.125

解答ステップ

z \to 2 lim ((\frac{2 z - z ^{2}}{z ^{2} - 4})^{3})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

不定形式の場合を除く

= (z \to 2 lim (\frac{2 z - z ^{2}}{z ^{2} - 4}))^{3}

簡素化

\frac{2 z - z ^{2}}{z ^{2} - 4} : - \frac{z}{z + 2}

= (z \to 2 lim (- \frac{z}{z + 2}))^{3}

値を挿入する

z = 2

= (- \frac{2}{2 + 2})^{3}

簡素化

(- \frac{2}{2 + 2})^{3} : - \frac{1}{8}

= - \frac{1}{8}

グラフ

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