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

Lösung

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

\infty

Schritte zur Lösung

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

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

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

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

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

= (- 1) (- \infty)

Wende die Unendlichkeitseigenschaft an:

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

= \infty

x \to 0 lim ([\frac{1}{x ^{2}} - \frac{1}{ln ( 1 + x ^{2} )}])

x \to 4 - lim (\frac{a x + b}{x + c})

x \to \infty lim (x^{2} + 3 x + 19 - x)

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

x \to \frac{π}{6} lim (sec^{2} (x))