limit as x approaches 0-of 1/(x^2)+1/x

Lösung

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

\infty

Schritte zur Lösung

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

Vereinfache

\frac{1}{x ^{2}} + \frac{1}{x} : \frac{1 + x}{x ^{2}}

= x \to 0 - lim (\frac{1 + x}{x ^{2}})

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

= x \to 0 - lim ((1 + x) \frac{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 0 - lim (1 + x) \cdot x \to 0 - lim (\frac{1}{x ^{2}})

x \to 0 - lim (1 + x) = 1

x \to 0 - lim (\frac{1}{x ^{2}}) = \infty

= 1 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

n \to \infty lim (4)

x \to 2 lim (23 + 7)

x \to \frac{1}{2} lim (3 x - 1)

x \to 5 lim (4 x + 3)

x \to \infty lim (\frac{x x}{x})