limit as x approaches 0 of (2^x+x)^{3/x}

Lösung

x \to 0 lim ((2^{x} + x)^{\frac{3}{x}})

e^{3 (l n (2) + 1)}

Dezimale

160.68429 \dots

Schritte zur Lösung

x \to 0 lim ((2^{x} + x)^{\frac{3}{x}})

Wende Exponentenregel an

= x \to 0 lim (e^{\frac{3}{x} l n (2^{x} + x)})

Wende die Kettenregel für Grenzen an:

e^{3 (l n (2) + 1)}

= e^{3 (l n (2) + 1)}

x \to 1 lim (ln (x) + 1)

x \to - 2 lim (x^{2} - 4 x + 1)

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

x \to 1 lim (\frac{7 x - 7}{8 x - 8})

x \to 0 lim (x^{2} \cdot ln ∣ x ∣)