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

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

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

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

- \infty

Solution steps

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

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

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

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

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

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

x \to 0 + lim (ln (2 x)) = - \infty

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

= \frac{1}{2} (- \infty) \cdot \infty

Apply Infinity Property:

\frac{1}{2} (- \infty) \infty = - \infty

= - \infty

x \to - 3 lim (2 x^{3} + 3 x^{2} - 11)

x \to 0 lim (x (b^{2} - x^{2}))

x \to 1 lim ((x + 1) (2 x + 3))

x \to 0 lim (\frac{( 2 + x ) ^{3}}{x})

x \to 0 lim (cos (e) c x - \frac{1}{x})

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