limit as x approaches 0 of (a^x-1)/(2x)

Lösung

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

\frac{1}{2} ln (a)

Schritte zur Lösung

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

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

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

Wende das L'Hopital Theorem an

= \frac{1}{2} \cdot x \to 0 lim (\frac{a ^{x} ln ( a )}{1})

Setze den Wert

x = 0

ein

= \frac{1}{2} \cdot \frac{a ^{0} ln ( a )}{1}

Vereinfache

\frac{1}{2} \cdot \frac{a ^{0} ln ( a )}{1} : \frac{1}{2} ln (a)

= \frac{1}{2} ln (a)

x \to - \infty lim (4 x^{3})

x \to 0 lim (\frac{8}{x + 2})

\frac{\partial}{\partial x} (x^{2} + y^{2} + 2)

d er i v a t i v e \frac{1}{b - m t}

n = 5 \sum \infty cos (\frac{1}{n ^{3}})