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Beliebt Rechnen >

limit as θ approaches 0 of (sin(5θ))/(θ+tan(7θ))

Lösung

θ \to 0 lim (\frac{sin ( 5 θ )}{θ + tan ( 7 θ )})

Lösung

\frac{5}{8}

+1

Dezimale

0.625

Schritte zur Lösung

θ \to 0 lim (\frac{sin ( 5 θ )}{θ + tan ( 7 θ )})

Wende das L'Hopital Theorem an

= θ \to 0 lim (\frac{cos ( 5 θ ) \cdot 5}{1 + sec ^{2} ( 7 θ ) \cdot 7})

Setze den Wert

θ = 0

ein

= \frac{cos ( 5 \cdot 0 ) \cdot 5}{1 + sec ^{2} ( 7 \cdot 0 ) \cdot 7}

Vereinfache

\frac{cos ( 5 \cdot 0 ) \cdot 5}{1 + sec ^{2} ( 7 \cdot 0 ) \cdot 7} : \frac{5}{8}

= \frac{5}{8}

Graph

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