limit as x approaches 0 of (4^x-1)/(5x)

Lösung

x \to 0 lim (\frac{4 ^{x} - 1}{5 x})

\frac{2}{5} ln (2)

Dezimale

0.27725 \dots

Schritte zur Lösung

x \to 0 lim (\frac{4 ^{x} - 1}{5 x})

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

= \frac{1}{5} \cdot x \to 0 lim (\frac{4 ^{x} - 1}{x})

Wende das L'Hopital Theorem an

= \frac{1}{5} \cdot x \to 0 lim (\frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1})

Setze den Wert

x = 0

ein

= \frac{1}{5} \cdot \frac{ln ( 2 ) \cdot 2 ^{2 \cdot 0 + 1}}{1}

Vereinfache

\frac{1}{5} \cdot \frac{ln ( 2 ) \cdot 2 ^{2 \cdot 0 + 1}}{1} : \frac{2}{5} ln (2)

= \frac{2}{5} ln (2)

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

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

x \to \infty - lim (cos (x))

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

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