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

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

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

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

0

Solution steps

x \to 0 + lim (\frac{e ^{x}}{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

= \frac{lim _{x \to 0 +} ( e ^{x} )}{lim _{x \to 0 +} ( ln ( x ) )}

x \to 0 + lim (e^{x}) = 1

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

= \frac{1}{- \infty}

Apply Infinity Property:

\frac{c}{- \infty} = 0

= 0

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