What is the limit as x approaches infinity of-x^x ?

The limit as x approaches infinity of-x^x is -infinity

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limit as x approaches infinity of-x^x

x \to \infty lim (- x^{x})

- \infty

Solution steps

x \to \infty lim (- x^{x})

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

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

Apply exponent rules

= - x \to \infty lim (e^{x l n (x)})

Apply the Limit Chain Rule:

\infty

= - \infty

x \to 0 lim (\frac{sin ( x ) cos ( x )}{x ( 1 + cos ( x ) )})

x \to 0 lim (x^{2} ln^{2} (x))

x \to \infty - lim (cos (x))

x \to \infty lim (\frac{- 3 x ^{3} + 7 x ^{2} - 6 x + 4}{- 3 x ^{2} + 5 x - 5})

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

What is the limit as x approaches infinity of-x^x ?
The limit as x approaches infinity of-x^x is -infinity