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

Lösung

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

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

Dezimale

29.55622 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Wende die Kettenregel für Grenzen an:

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

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

x \to 3 lim (\frac{4}{( x - 3 ) ^{2}})

x \to 0 lim (\frac{2 x - arcsin ( x )}{2 x + arctan ( x )})

x \to 0 + lim (x^{2} ln (4 x^{2}))

x \to 2 lim (\frac{sin ( x - 2 )}{3 x - 6})

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