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Beliebt Rechnen >

limit as x approaches 0-of 1/x-1/(|x|)

Lösung

x \to 0 - lim (\frac{1}{x} - \frac{1}{∣ x ∣})

Lösung

- \infty

Schritte zur Lösung

x \to 0 - lim (\frac{1}{x} - \frac{1}{∣ x ∣})

x

ist negativ wenn

x \to 0 -

. Deshalb

∣ x ∣ = - x

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

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

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

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

= - \infty - \infty

Wende die Unendlichkeitseigenschaft an:

- \infty - \infty = - \infty

= - \infty

Graph

Beliebte Beispiele

derivative of x^3-2x^2+x+1

\frac{d}{d x} (x^{3} - 2 x^{2} + x + 1)

(\partial)/(\partial x)((e^x)/(y+x^3))

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{3}})

derivative of tan(pi/4)

\frac{d}{d x} (tan (\frac{π}{4}))

integral of (x^3)/((x^2+4)^2)

\int \frac{x ^{3}}{( x ^{2} + 4 ) ^{2}} d x

limit as x approaches infinity of x^8

x \to \infty lim (x^{8})