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Beliebt Rechnen >

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

Lösung

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

Lösung

- 1

Schritte zur Lösung

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

Multipliziere aus

\frac{1 - cot ( x )}{\frac{1}{x}} : x - x cot (x)

= x \to 0 lim (x - x cot (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 (x) - x \to 0 lim (x cot (x))

x \to 0 lim (x) = 0

x \to 0 lim (x cot (x)) = 1

= 0 - 1

Vereinfache

= - 1

Graph

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