limit as y approaches 0 of 2/(y^2+y)-2/y

解

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

- 2

解答ステップ

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

\frac{2}{y ^{2} + y} - \frac{2}{y}

の共役で乗じる

\frac{\frac{4}{y ^{4} + 2 y ^{3} + y ^{2}} - \frac{4}{y ^{2}}}{\frac{2}{y ^{2} + y} + \frac{2}{y}}

= y \to 0 lim (\frac{\frac{4}{y ^{4} + 2 y ^{3} + y ^{2}} - \frac{4}{y ^{2}}}{\frac{2}{y ^{2} + y} + \frac{2}{y}})

簡素化

\frac{\frac{4}{y ^{4} + 2 y ^{3} + y ^{2}} - \frac{4}{y ^{2}}}{\frac{2}{y ^{2} + y} + \frac{2}{y}} : - \frac{2}{y + 1}

= y \to 0 lim (- \frac{2}{y + 1})

値を挿入する

y = 0

= - \frac{2}{0 + 1}

簡素化

= - 2