limit as x approaches-1-of (x^3)/(x^2-1)

Lösung

x \to - 1 - lim (\frac{x ^{3}}{x ^{2} - 1})

- \infty

Schritte zur Lösung

x \to - 1 - lim (\frac{x ^{3}}{x ^{2} - 1})

\frac{x ^{3}}{x ^{2} - 1} = x^{3} \frac{1}{x ^{2} - 1}

= x \to - 1 - lim (x^{3} \frac{1}{x ^{2} - 1})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

= x \to - 1 - lim (x^{3}) \cdot x \to - 1 - lim (\frac{1}{x ^{2} - 1})

x \to - 1 - lim (x^{3}) = - 1

x \to - 1 - lim (\frac{1}{x ^{2} - 1}) = \infty

= (- 1) \cdot \infty

Wende die Unendlichkeitseigenschaft an:

- c \cdot \infty = - \infty

= - \infty

x \to 1 - lim (ln (x) \cdot ln (1 - x))

x \to 3 lim (x^{2} - x)

z \to 2 lim (\frac{z ^{3} - 8}{z - 2})

x \to \frac{π}{2} + lim (\frac{tan ( x )}{x})

x \to 2 lim (3 x^{3} + 2 x - 1)