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

Lösung

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

\infty

Schritte zur Lösung

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

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

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

x \to 2 + lim (x^{2} + 4) = 8

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

= 8 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

x \to - 4 lim (16 - x^{2})

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

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

x \to - 1 lim (\frac{x ^{2} - 9}{x - 3})

x \to 1 lim (\frac{97 π x}{1 - x})