limit as x approaches-2-of (x+4)/(x^2-4)

Lösung

x \to - 2 - lim (\frac{x + 4}{x ^{2} - 4})

\infty

Schritte zur Lösung

x \to - 2 - lim (\frac{x + 4}{x ^{2} - 4})

\frac{x + 4}{x ^{2} - 4} = (x + 4) \frac{1}{x ^{2} - 4}

= x \to - 2 - lim ((x + 4) \frac{1}{x ^{2} - 4})

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 + 4) \cdot x \to - 2 - lim (\frac{1}{x ^{2} - 4})

x \to - 2 - lim (x + 4) = 2

x \to - 2 - lim (\frac{1}{x ^{2} - 4}) = \infty

= 2 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

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

x \to 0 lim ((1 + \frac{x}{5})^{\frac{1}{x}})

x \to 6 lim (2 x^{2} + 4)

x \to 0 - lim (x^{4} sin (\frac{1}{x}))

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