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

is positive when

x \to \infty

. Therefore

∣ x ∣ = 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 (x^{\frac{x}{2}})

x \to π + lim (cot (2 x - π))

x \to 9 lim (9483)

x \to - 3 lim (\frac{x}{x ^{3} + 8})

x \to 0 lim (\frac{sin ( 5 )}{x})

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