limit as x approaches 3+of (x^2+9)/(x-3)

Lösung

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

\infty

Schritte zur Lösung

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

\frac{x ^{2} + 9}{x - 3} = (x^{2} + 9) \frac{1}{x - 3}

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

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

x \to 3 + lim (x^{2} + 9) = 18

x \to 3 + lim (\frac{1}{x - 3}) = \infty

= 18 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

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