limit as x approaches infinity of (1+3/x)^{x/4}

Lösung

x \to \infty lim ((1 + \frac{3}{x})^{\frac{x}{4}})

e^{\frac{3}{4}}

Dezimale

2.11700 \dots

Schritte zur Lösung

x \to \infty lim ((1 + \frac{3}{x})^{\frac{x}{4}})

Wende Exponentenregel an

= x \to \infty lim (e^{\frac{x}{4} l n (1 + \frac{3}{x})})

Wende die Kettenregel für Grenzen an:

e^{\frac{3}{4}}

= e^{\frac{3}{4}}

d er i v a t i v e h (x) = ln (x + x^{2} - 7)

in v erse l a pl a ce \frac{- 2 s + 1}{s ^{2} + 2 s - 8}

x \to 0 lim (\frac{x + 4}{x})

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 9 y^{3})

a re a x^{3}, - x, 1