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

Lösung

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

- \infty

Schritte zur Lösung

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

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

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

x \to 3 - lim (x + 2) = 5

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

= 5 (- \infty)

Wende die Unendlichkeitseigenschaft an:

c \cdot (- \infty) = - \infty

= - \infty

x \to - 4 lim ((10 + 4)^{2})

x \to - \frac{3 π}{2} lim (tan (x))

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

x \to 3 lim (f (x) + g (x))

x \to \infty lim (\frac{c}{x})