limit as x approaches-3-of (x+1)/(x^2-9)

Lösung

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

- \infty

Schritte zur Lösung

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

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

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

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

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

= (- 2) \cdot \infty

Wende die Unendlichkeitseigenschaft an:

- c \cdot \infty = - \infty

= - \infty

x \to π lim (sin^{2} (x))

x \to 0 lim (x^{2} + 3 x - 4)

x \to 4 lim ((4 - x) \cdot ln (x - 4))

x \to 3 lim (\frac{x ^{3} - 2 x ^{2} - 4 x + 8}{3 x ^{2} + 3 x - 6})

x \to \infty lim (\frac{3 x ^{3} - 4 x ^{2} + 2}{x ^{3} + 2 x + 7})