What is the limit as x approaches (infinity) of (ln(x))/(sqrt(x)) ?

The limit as x approaches (infinity) of (ln(x))/(sqrt(x)) is 0

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limit as x approaches (infinity) of (ln(x))/(sqrt(x))

x \to (\infty) lim (\frac{ln ( x )}{x})

0

Solution steps

x \to \infty lim (\frac{ln ( x )}{x})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{\frac{1}{x}}{\frac{1}{2 x}})

= x \to \infty lim (\frac{\frac{1}{x}}{\frac{1}{2 x}})

Simplify

\frac{\frac{1}{x}}{\frac{1}{2 x}} : \frac{2}{x}

= x \to \infty lim (\frac{2}{x})

Apply Infinity Property:

x \to \infty lim (\frac{c}{x ^{a}}) = 0

= 0

x \to 1 lim (\frac{( x ^{2} )}{x - 1})

\int_{0}^{1} \frac{3 x ^{2}}{1 + x ^{3}} d x

x^{2} y^{^{''}} - 3 x y^{^{'}} + 5 y = 0

f (x) = 2 x^{2} - 9 x + 10, at x = 2

\frac{d}{d x} (x arcsin (x))

What is the limit as x approaches (infinity) of (ln(x))/(sqrt(x)) ?
The limit as x approaches (infinity) of (ln(x))/(sqrt(x)) is 0