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Beliebt Rechnen >

limit as x approaches 0 of (sin(2x))/(arcsin(x))

Lösung

x \to 0 lim (\frac{sin ( 2 x )}{arcsin ( x )})

Lösung

2

Schritte zur Lösung

x \to 0 lim (\frac{sin ( 2 x )}{arcsin ( x )})

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

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

Vereinfache

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

= 2

Graph

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