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

Lösung

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

\infty

Schritte zur Lösung

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

\frac{x ^{2}}{x - 1} = x^{2} \frac{1}{x - 1}

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

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}{x - 1})

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

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

= 1 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

x \to 0 lim (ln (x + 2))

t \to 0 lim (\frac{e ^{t}}{ln ( t )})

n \to \infty lim (t^{n})

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

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