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Beliebt Rechnen >

limit as x approaches pi/6 of (sin(x)-sin(pi/6))/(x-pi/6)

Lösung

x \to \frac{π}{6} lim (\frac{sin ( x ) - sin ( \frac{π}{6} )}{x - \frac{π}{6}})

Lösung

\frac{3}{2}

+1

Dezimale

0.86602 \dots

Schritte zur Lösung

x \to \frac{π}{6} lim (\frac{sin ( x ) - sin ( \frac{π}{6} )}{x - \frac{π}{6}})

Wende das L'Hopital Theorem an

= x \to \frac{π}{6} lim (\frac{cos ( x )}{1})

Setze den Wert

x = \frac{π}{6}

ein

= \frac{cos ( \frac{π}{6} )}{1}

Vereinfache

\frac{cos ( \frac{π}{6} )}{1} : \frac{3}{2}

= \frac{3}{2}

Graph

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