limit as x approaches 0 of (2x-arcsin(x))/(2x+arctan(x))

Lösung

x \to 0 lim (\frac{2 x - arcsin ( x )}{2 x + arctan ( x )})

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

x \to 0 lim (\frac{2 x - arcsin ( x )}{2 x + arctan ( x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{2 - \frac{1}{1 - x ^{2}}}{2 + \frac{1}{x ^{2} + 1}})

Setze den Wert

x = 0

ein

= \frac{2 - \frac{1}{1 - 0 ^{2}}}{2 + \frac{1}{0 ^{2} + 1}}

Vereinfache

\frac{2 - \frac{1}{1 - 0 ^{2}}}{2 + \frac{1}{0 ^{2} + 1}} : \frac{1}{3}

= \frac{1}{3}

x \to 0 + lim (x^{2} ln (4 x^{2}))

x \to 2 lim (\frac{sin ( x - 2 )}{3 x - 6})

x \to 0 + lim (x^{2} csc^{2} (3 x))

x \to 0 + lim (x^{\frac{1}{f ( x )}})

x \to 0 - lim ((1 - e^{x})^{x})