limit as x approaches 0 of (7^x-1)/(5x)

Lösung

x \to 0 lim (\frac{7 ^{x} - 1}{5 x})

\frac{1}{5} ln (7)

Dezimale

0.38918 \dots

Schritte zur Lösung

x \to 0 lim (\frac{7 ^{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{7 ^{x} - 1}{x})

Wende das L'Hopital Theorem an

= \frac{1}{5} \cdot x \to 0 lim (\frac{ln ( 7 ) \cdot 7 ^{x}}{1})

Setze den Wert

x = 0

ein

= \frac{1}{5} \cdot \frac{ln ( 7 ) \cdot 7 ^{0}}{1}

Vereinfache

\frac{1}{5} \cdot \frac{ln ( 7 ) \cdot 7 ^{0}}{1} : \frac{1}{5} ln (7)

= \frac{1}{5} ln (7)

x \to 2 lim (\frac{7}{x - 1})

x \to 3 - lim ((x) + (4 - x))

x \to - \frac{π}{2} lim (cos (x))

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

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