What is the limit as x approaches infinity of (ln(x))/(x^{(1/2))} ?

The limit as x approaches infinity of (ln(x))/(x^{(1/2))} is 0

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limit as x approaches infinity of (ln(x))/(x^{(1/2))}

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

0

Solution steps

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

Apply L'Hopital's Rule

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

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

Simplify

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

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

Apply Infinity Property:

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

= 0

x \to 3 lim (- \frac{x ^{4}}{3} + \frac{x}{2})

x \to 0 lim (4 x^{3} + 3 x)

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

n \to \infty lim (n \cdot x)

x \to 0 - lim (\frac{- x}{x})

What is the limit as x approaches infinity of (ln(x))/(x^{(1/2))} ?
The limit as x approaches infinity of (ln(x))/(x^{(1/2))} is 0