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

Lösung

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

\infty

Schritte zur Lösung

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

\frac{x ^{2}}{ln ( x )} = x^{2} \frac{1}{ln ( x )}

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

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

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

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

= 1 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

x \to \frac{π}{2} lim ((sin^{2} (x))^{t a n (x)})

x \to - 1 lim (7)

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

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

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