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Beliebt Rechnen >

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

Lösung

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

Lösung

3

Schritte zur Lösung

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

mit Einschränkung des unbestimmten Ausdrucks

= \frac{lim _{x \to - \infty} ( 4 e ^{\frac{1}{x}} - 1 )}{lim _{x \to - \infty} ( 1 + e ^{x} )}

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

x \to - \infty lim (1 + e^{x}) = 1

= \frac{3}{1}

Vereinfache

= 3

Graph

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