limit as x approaches-5-of (4x^2-12)/(x+5)

Lösung

x \to - 5 - lim (\frac{4 x ^{2} - 12}{x + 5})

- \infty

Schritte zur Lösung

x \to - 5 - lim (\frac{4 x ^{2} - 12}{x + 5})

\frac{4 x ^{2} - 12}{x + 5} = (4 x^{2} - 12) \frac{1}{x + 5}

= x \to - 5 - lim ((4 x^{2} - 12) \frac{1}{x + 5})

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 - 5 - lim (4 x^{2} - 12) \cdot x \to - 5 - lim (\frac{1}{x + 5})

x \to - 5 - lim (4 x^{2} - 12) = 88

x \to - 5 - lim (\frac{1}{x + 5}) = - \infty

= 88 (- \infty)

Wende die Unendlichkeitseigenschaft an:

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

= - \infty

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

x \to \infty lim ((cos (x))^{\frac{1}{( x ^{2} )}})

x \to 1 lim (\frac{x ^{11} + 2 x - 3}{x ^{7} + x ^{2} - x - 1})

x \to 0 lim (cos (x))

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