limit as x approaches 0 of (e^x-1)/(9x)

Lösung

x \to 0 lim (\frac{e ^{x} - 1}{9 x})

\frac{1}{9}

Dezimale

0.11111 \dots

Schritte zur Lösung

x \to 0 lim (\frac{e ^{x} - 1}{9 x})

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

= \frac{1}{9} \cdot x \to 0 lim (\frac{e ^{x} - 1}{x})

Wende das L'Hopital Theorem an

= \frac{1}{9} \cdot x \to 0 lim (\frac{e ^{x}}{1})

Setze den Wert

x = 0

ein

= \frac{1}{9} \cdot \frac{e ^{0}}{1}

Vereinfache

\frac{1}{9} \cdot \frac{e ^{0}}{1} : \frac{1}{9}

= \frac{1}{9}

\frac{d y}{d x} = 6 x^{2} + 3

in v erse l a pl a ce \frac{( 4 s - 5 )}{s ^{2} - 6 s + 13}

n = 1 \sum \infty (\frac{1}{3})^{n}

a re a 4 x^{2}, \frac{x}{4}

a re a y = x^{2} + 4, y = - x^{2} - 1, x = - 2, x = 3