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

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

limit as x approaches 0+of (ln(x))/(sqrt(x))

x \to 0 + lim (\frac{ln ( x )}{x})

- \infty

Solution steps

x \to 0 + lim (\frac{ln ( x )}{x})

\frac{ln ( x )}{x} = ln (x) \frac{1}{x}

= x \to 0 + lim (ln (x) \frac{1}{x})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 + lim (ln (x)) \cdot x \to 0 + lim (\frac{1}{x})

x \to 0 + lim (ln (x)) = - \infty

x \to 0 + lim (\frac{1}{x}) = \infty

= (- \infty) \cdot \infty

Apply Infinity Property:

(- \infty) \infty = - \infty

= - \infty

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 cos (2 t) e^{- t}

\int \frac{1}{cos ^{5} ( x )} d x

\frac{2}{x ^{\frac{1}{3}}} - 2

2 y^{^{'}} + t y = 7

\frac{d}{d x} (\frac{3 x - 1}{2 x + 5})

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