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

Lösung

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

\infty

Schritte zur Lösung

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

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

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

x \to 2 + lim (3 - x) = 1

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

= 1 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

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

x \to 1 lim (x^{2} - 5 x + 6)

x \to \infty - lim (x)

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

x \to 0 lim (cos (\frac{2}{x}) x^{4})