limit as x approaches 1+of (x+5)/(1-x^2)

Lösung

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

- \infty

Schritte zur Lösung

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

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

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

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

x \to 1 + lim (x + 5) = 6

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

= 6 (- \infty)

Wende die Unendlichkeitseigenschaft an:

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

= - \infty

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

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

x \to \infty lim ((\frac{2 ln ( x )}{ln ( 7 x ^{2} )})^{l n (x)})

x \to - 6 lim (\frac{4}{x + 6})

x \to \frac{π}{6} lim (2^{s i n (x)})