What is the limit as x approaches 0+of (ln(x))/(x^3) ?

The limit as x approaches 0+of (ln(x))/(x^3) is -infinity

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limit as x approaches 0+of (ln(x))/(x^3)

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

- \infty

Solution steps

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

\frac{ln ( x )}{x ^{3}} = ln (x) \frac{1}{x ^{3}}

= x \to 0 + lim (ln (x) \frac{1}{x ^{3}})

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 ^{3}})

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

x \to 0 + lim (\frac{1}{x ^{3}}) = \infty

= (- \infty) \cdot \infty

Apply Infinity Property:

(- \infty) \infty = - \infty

= - \infty

\frac{x}{x + 2}

\int x^{\frac{5}{3}} ln (x) d x

f (x) = x^{2} + 11 x - 15, at x = 1

\int 2 x^{3} \cdot cos (x^{2}) d x

\frac{d}{d x} (- 4 x - 3)

What is the limit as x approaches 0+of (ln(x))/(x^3) ?
The limit as x approaches 0+of (ln(x))/(x^3) is -infinity