What is the limit as x approaches infinity of x^{sqrt(x)} ?

The limit as x approaches infinity of x^{sqrt(x)} is infinity

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limit as x approaches infinity of x^{sqrt(x)}

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

\infty

Solution steps

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

\int \frac{2}{x x ^{2} - 4} d x

\int_{3}^{4} - lo g_{9} (x) d x

\int 2 x^{2} + \frac{1}{( 2 x ) ^{2}} d x

\frac{\partial}{\partial y} (x y e^{9 y})

y \to + 0 lim (\frac{y}{sin ( 5 y )})

What is the limit as x approaches infinity of x^{sqrt(x)} ?
The limit as x approaches infinity of x^{sqrt(x)} is infinity