limit as h approaches 0 of (cos(pi/6+h)-(sqrt(3))/2)/(h)

Lösung

h \to 0 lim (\frac{cos ( \frac{π}{6} + h ) - \frac{3}{2}}{h})

- \frac{1}{2}

Dezimale

- 0.5

Schritte zur Lösung

h \to 0 lim (\frac{cos ( \frac{π}{6} + h ) - \frac{3}{2}}{h})

Wende das L'Hopital Theorem an

= h \to 0 lim (\frac{- sin ( h + \frac{π}{6} )}{1})

Setze den Wert

h = 0

ein

= \frac{- sin ( 0 + \frac{π}{6} )}{1}

Vereinfache

\frac{- sin ( 0 + \frac{π}{6} )}{1} : - \frac{1}{2}

= - \frac{1}{2}

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