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

Lösung

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

\infty

Schritte zur Lösung

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

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

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

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

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

= 6 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

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

x \to 4 lim ([\frac{x ^{2} + 4}{5}])

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

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

x \to π lim (sin (\frac{x}{2} - π))