What is the limit as x approaches infinity of x^{3x} ?

The limit as x approaches infinity of x^{3x} is infinity

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limit as x approaches infinity of x^{3x}

x \to \infty lim (x^{3 x})

\infty

Solution steps

x \to \infty lim (x^{3 x})

Apply exponent rules

= x \to \infty lim (e^{3 x l n (x)})

Apply the Limit Chain Rule:

\infty

= \infty

y^{^{'}} - \frac{y}{x} = - x

y = \frac{ln ( e ^{x} )}{x}

\frac{d}{d x} (3 x^{2} ln (x))

f (x) = \frac{3}{8 x}

\frac{d}{d x} (e^{x} (sin (x) - cos (x)))

What is the limit as x approaches infinity of x^{3x} ?
The limit as x approaches infinity of x^{3x} is infinity