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Beliebt Rechnen >

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

Lösung

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

Lösung

- 1

Schritte zur Lösung

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Vereinfache

\frac{1 ^{x + 1} x}{x + x} : \frac{x}{x + 1}

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

Dividiere durch

x : \frac{1}{1 + \frac{1}{x}}

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

x \to \infty lim (1) = 1

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

= - \frac{1}{1}

Vereinfache

= - 1

Graph

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