limit as x approaches pi/4 of (ln(tan(x)))/(1-cot(x))

Lösung

x \to \frac{π}{4} lim (\frac{ln ( tan ( x ) )}{1 - cot ( x )})

1

Schritte zur Lösung

x \to \frac{π}{4} lim (\frac{ln ( tan ( x ) )}{1 - cot ( x )})

Wende das L'Hopital Theorem an

= x \to \frac{π}{4} lim (\frac{2 csc ( 2 x )}{csc ^{2} ( x )})

Setze den Wert

x = \frac{π}{4}

ein

= \frac{2 csc ( 2 \cdot \frac{π}{4} )}{csc ^{2} ( \frac{π}{4} )}

Vereinfache

\frac{2 csc ( 2 \cdot \frac{π}{4} )}{csc ^{2} ( \frac{π}{4} )} : 1

= 1

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