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人気のある微分積分 >

limit as z approaches i of (z-i)/(z^2+1)

解

z \to i lim (\frac{z - i}{z ^{2} + 1})

解

- \frac{i}{2}

解答ステップ

z \to i lim (\frac{z - i}{z ^{2} + 1})

z - i

の共役で乗じる

\frac{z ^{2} + 1}{z + i}

= z \to i lim (\frac{\frac{z ^{2} + 1}{z + i}}{z ^{2} + 1})

簡素化

\frac{\frac{z ^{2} + 1}{z + i}}{z ^{2} + 1} : \frac{1}{z + i}

= z \to i lim (\frac{1}{z + i})

値を挿入する

z = i

= \frac{1}{i + i}

簡素化

\frac{1}{i + i} : - \frac{i}{2}

= - \frac{i}{2}

グラフ

人気の例

limit as x approaches infinity of x(pi/4-arctan(x/(x+1)))

x \to \infty lim (x (\frac{π}{4} - arctan (\frac{x}{x + 1})))

limit as x approaches 0+of 2cos(x)

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