What is the limit as x approaches 0+of (ln(x))/(x^2) ?

The limit as x approaches 0+of (ln(x))/(x^2) is -infinity

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limit as x approaches 0+of (ln(x))/(x^2)

x \to 0 + lim (\frac{ln ( x )}{x ^{2}})

- \infty

Solution steps

x \to 0 + lim (\frac{ln ( x )}{x ^{2}})

\frac{ln ( x )}{x ^{2}} = ln (x) \frac{1}{x ^{2}}

= x \to 0 + lim (ln (x) \frac{1}{x ^{2}})

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 ^{2}})

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

x \to 0 + lim (\frac{1}{x ^{2}}) = \infty

= (- \infty) \cdot \infty

Apply Infinity Property:

(- \infty) \infty = - \infty

= - \infty

\frac{d y}{d t} = 5 y + y^{5}

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

y = x^{2} - 2 x - 3

\frac{d y}{d x} = \frac{x y}{8}

x^{2} + 2 x + 4

What is the limit as x approaches 0+of (ln(x))/(x^2) ?
The limit as x approaches 0+of (ln(x))/(x^2) is -infinity