limit as x approaches 0 of (xe^x)/(sin(x))

Lösung

x \to 0 lim (\frac{x e ^{x}}{sin ( x )})

1

Schritte zur Lösung

x \to 0 lim (\frac{x e ^{x}}{sin ( x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{e ^{x} + e ^{x} x}{cos ( x )})

Setze den Wert

x = 0

ein

= \frac{e ^{0} + e ^{0} \cdot 0}{cos ( 0 )}

Vereinfache

\frac{e ^{0} + e ^{0} \cdot 0}{cos ( 0 )} : 1

= 1

n = 1 \sum \infty 1 (\frac{5}{6})^{n}

k = 1 \sum \infty cos (\frac{1}{k}) - cos (\frac{1}{k + 1})

n = 0 \sum \infty \frac{( 3 ^{n} )}{2}

\int \frac{9}{x ^{2} ( x ^{2} + 25 )} d x

\frac{d x}{d t} = 6 - \frac{3 x}{500}