limit as x approaches 3-of (x-5)/(x^2-9)

Lösung

x \to 3 - lim (\frac{x - 5}{x ^{2} - 9})

\infty

Schritte zur Lösung

x \to 3 - lim (\frac{x - 5}{x ^{2} - 9})

\frac{x - 5}{x ^{2} - 9} = (x - 5) \frac{1}{x ^{2} - 9}

= x \to 3 - lim ((x - 5) \frac{1}{x ^{2} - 9})

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

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

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

= (- 2) (- \infty)

Wende die Unendlichkeitseigenschaft an:

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

= \infty

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

n \to 1 lim (ln (n))

x \to 0 lim (3 - 2 x - x^{2})

x \to - 3 lim ((x + 3)^{2} - 4)

x \to 3 lim (4)