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Beliebt Rechnen >

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

Lösung

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

Lösung

e^{a^{2}}

Schritte zur Lösung

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

Wende Exponentenregel an

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

Wende die Kettenregel für Grenzen an:

e^{a^{2}}

= e^{a^{2}}

Graph

Beliebte Beispiele

fläche x=3-3y^2,x=3y^2-3

a re a x = 3 - 3 y^{2}, x = 3 y^{2} - 3

integral of (2x)/((x-5)^2)

\int \frac{2 x}{( x - 5 ) ^{2}} d x

derivative of ln(sqrt(4+5x))

\frac{d}{d x} (ln (4 + 5 x))

derivative of ax^n+cy(x^n)

\frac{d}{d x} (a x^{n} + cy (x)^{n})

derivative x/(3sqrt(1+x^2))

d er i v a t i v e \frac{x}{3 1 + x ^{2}}