limit as x approaches pi of ((e^{sin(x)}-1))/(x-pi)

Lösung

x \to π lim (\frac{( e ^{s i n (x)} - 1 )}{x - π})

- 1

Schritte zur Lösung

x \to π lim (\frac{e ^{s i n (x)} - 1}{x - π})

Wende das L'Hopital Theorem an

= x \to π lim (\frac{e ^{s i n (x)} cos ( x )}{1})

Setze den Wert

x = π

ein

= \frac{e ^{s i n (π)} cos ( π )}{1}

Vereinfache

\frac{e ^{s i n (π)} cos ( π )}{1} : - 1

= - 1

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