limit as θ approaches 0 of (cos(θ)tan(θ))/θ

Lösung

θ \to 0 lim (\frac{cos ( θ ) tan ( θ )}{θ})

1

Schritte zur Lösung

θ \to 0 lim (\frac{cos ( θ ) tan ( θ )}{θ})

cos (θ) tan (θ) = sin (θ)

= θ \to 0 lim (\frac{sin ( θ )}{θ})

Wende das L'Hopital Theorem an

= θ \to 0 lim (\frac{cos ( θ )}{1})

Setze den Wert

θ = 0

ein

= \frac{cos ( 0 )}{1}

Vereinfache

\frac{cos ( 0 )}{1} : 1

= 1

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