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

Lösung

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

- 2

Schritte zur Lösung

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

Multipliziere mit der Konjugation von

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

Vereinfache

\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})

Setze den Wert

y = 0

ein

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

Vereinfache

= - 2

d er i v a t i v e f (x) = 2^{l n (x)}

a re a 6 x^{2} - 9 x - 6, 7 x^{2} - 5 x - 3

x \to 0 lim (\frac{x}{5})

d er i v a t i v e (x^{2} - 9)^{2} + 2

7 x (x + 3 y) y^{^{'}} = 7 y (x - 3 y)