limit as x approaches 0 of (2tan(x/2))/x

Lösung

x \to 0 lim (\frac{2 tan ( \frac{x}{2} )}{x})

1

Schritte zur Lösung

x \to 0 lim (\frac{2 tan ( \frac{x}{2} )}{x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to 0 lim (\frac{tan ( \frac{x}{2} )}{x})

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

= 2 \cdot \frac{sec ^{2} ( \frac{0}{2} ) \frac{1}{2}}{1}

Vereinfache

2 \cdot \frac{sec ^{2} ( \frac{0}{2} ) \frac{1}{2}}{1} : 1

= 1

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