limit as x approaches 0 of (2e^x-2)/(3x)

Lösung

x \to 0 lim (\frac{2 e ^{x} - 2}{3 x})

\frac{2}{3}

Dezimale

0.66666 \dots

Schritte zur Lösung

x \to 0 lim (\frac{2 e ^{x} - 2}{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{2 e ^{x} - 2}{x})

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

= \frac{1}{3} \cdot \frac{2 e ^{0}}{1}

Vereinfache

\frac{1}{3} \cdot \frac{2 e ^{0}}{1} : \frac{2}{3}

= \frac{2}{3}

d er i v a t i v e t e^{\frac{- t}{2}}

\int \frac{1}{x ( x ^{2} - 81 ) ^{\frac{3}{2}}} d x

x \to \infty lim (f (x))

\frac{d}{d x} (3 x^{2} sin (x) + 3 x cos (x))

\frac{d}{d t} (a cos (3 t) + b sin (3 t))