limit as x approaches-2+of (x^2-x)/(x+2)

Lösung

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

\infty

Schritte zur Lösung

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

\frac{x ^{2} - x}{x + 2} = (x^{2} - x) \frac{1}{x + 2}

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

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

x \to - 2 + lim (x^{2} - x) = 6

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

= 6 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

x \to 0 lim ((1 - x) \frac{1}{x})

x \to 4 lim (\frac{1}{x})

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

x \to 0 + lim (\frac{1}{x} - \frac{1}{1 - e ^{x}})

x \to - 3 lim (4^{x})