limit as x approaches 0 of ((a^x+b^x)/2)^{1/x}

Lösung

x \to 0 lim ((\frac{a ^{x} + b ^{x}}{2})^{\frac{1}{x}})

e^{\frac{l n ( a ) + l n ( b )}{2}}

Schritte zur Lösung

x \to 0 lim ((\frac{a ^{x} + b ^{x}}{2})^{\frac{1}{x}})

Wende Exponentenregel an

= x \to 0 lim (e^{\frac{1}{x} l n (\frac{a ^{x} + b ^{x}}{2})})

Wende die Kettenregel für Grenzen an:

e^{\frac{l n ( a ) + l n ( b )}{2}}

= e^{\frac{l n ( a ) + l n ( b )}{2}}

x \to 0 + lim (2 x ln (x))

x \to 0 lim (\frac{( x - 3 ) ^{2} - 9}{x})

x \to 0 + lim ((tan (x))^{s i n (x)})

x \to 0 + lim ((1 - 3 x)^{\frac{2}{x}})

x \to e + lim (\frac{1}{x ln ( x - 1 )})