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

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

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

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

0

Solution steps

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

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

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

x \to 0 + lim (1) = 1

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

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

Simplify

2 \cdot \frac{1}{- \infty} : 0

= 0

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