limit as x approaches 0 of (9^x+x)^{2/x}

Lösung

x \to 0 lim ((9^{x} + x)^{\frac{2}{x}})

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

Dezimale

598.51354 \dots

Schritte zur Lösung

x \to 0 lim ((9^{x} + x)^{\frac{2}{x}})

Wende Exponentenregel an

= x \to 0 lim (e^{\frac{2}{x} l n (9^{x} + x)})

Wende die Kettenregel für Grenzen an:

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

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

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

x \to 1 lim ([\frac{x ^{3} - 1}{x ^{2} - 1}])

x \to 1 lim (\frac{5 x + 3 x - 2}{x ^{2} - 1})

x \to 0 lim (\frac{( 1 - cos ^{2} ( x ) )}{ln ( 1 + x ^{2} )})

x \to 0 lim (x^{9} e^{- x^{8}})