limit as x approaches 0 of (1-e^x)/(3x)

Lösung

x \to 0 lim (\frac{1 - e ^{x}}{3 x})

- \frac{1}{3}

Dezimale

- 0.33333 \dots

Schritte zur Lösung

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

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

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

Vereinfache

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

= - \frac{1}{3}

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

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

x \to 0 + lim (tan (x) (ln (x)))

x \to 0 + lim (\frac{x}{sin ( 8 x )})

x \to - 3 lim (5 x + 9)