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

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

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

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

\infty

Solution steps

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

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

= - 3 \cdot x \to 0 + lim (\frac{ln ( x )}{x})

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

= - 3 \cdot 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

= - 3 \cdot 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

= - 3 (- \infty) \cdot \infty

Apply Infinity Property:

- 3 (- \infty) \infty = \infty

= \infty

\int \frac{2 ^{x}}{ln ( 2 )} d x

\int \frac{1}{( x ) ^{2}} d x

\int x 3 - x^{2} d x

x \to \infty lim (π^{\infty})

\int (x + 3)^{2} d x

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