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Beliebt Rechnen >

limit as x approaches infinity of e^{5xln(1+1/x)}

Lösung

x \to \infty lim (e^{5 x l n (1 + \frac{1}{x})})

Lösung

e^{5}

+1

Dezimale

148.41315 \dots

Schritte zur Lösung

x \to \infty lim (e^{5 x l n (1 + \frac{1}{x})})

Vereinfache

e^{5 x l n (1 + \frac{1}{x})} : (1 + \frac{1}{x})^{5 x}

= x \to \infty lim ((1 + \frac{1}{x})^{5 x})

Wende Exponentenregel an

= x \to \infty lim (e^{5 x l n (1 + \frac{1}{x})})

Wende die Kettenregel für Grenzen an:

e^{5}

= e^{5}

Graph

Beliebte Beispiele

integral of (4x^3-5sqrt(x))/x

\int \frac{4 x ^{3} - 5 x}{x} d x

(\partial)/(\partial x)(r/x)

\frac{\partial}{\partial x} (\frac{r}{x})

integral of 1/(x^2sqrt(64x^2+81))

\int \frac{1}{x ^{2} 64 x ^{2} + 81} d x

(dy)/(dx)=((x-1))/(y-4)

\frac{d y}{d x} = \frac{( x - 1 )}{y - 4}

derivative y= 1/2 x+8

d er i v a t i v e y = \frac{1}{2} x + 8