limit as x approaches 0 of (arcsin(2x))/(3x)

Lösung

x \to 0 lim (\frac{arcsin ( 2 x )}{3 x})

\frac{2}{3}

Dezimale

0.66666 \dots

Schritte zur Lösung

x \to 0 lim (\frac{arcsin ( 2 x )}{3 x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{3} \cdot x \to 0 lim (\frac{arcsin ( 2 x )}{x})

Wende das L'Hopital Theorem an

= \frac{1}{3} \cdot x \to 0 lim (\frac{\frac{2}{1 - 4 x ^{2}}}{1})

Setze den Wert

x = 0

ein

= \frac{1}{3} \cdot \frac{\frac{2}{1 - 4 \cdot 0 ^{2}}}{1}

Vereinfache

\frac{1}{3} \cdot \frac{\frac{2}{1 - 4 \cdot 0 ^{2}}}{1} : \frac{2}{3}

= \frac{2}{3}

x \to 0 + lim (x cos (x))

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

x \to 2 lim (\frac{3 x}{x + 2})

x \to \infty lim (3 (x)^{2})

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