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

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

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

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

0

Solution steps

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

x \to 0 + lim (x) = 0

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

= \frac{0}{- \infty}

Apply Infinity Property:

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

= 0

f (x) = x^{2} + 4 x - 5, - 3, 3

x \to 3 lim (\frac{5 x}{x - 3})

\frac{d}{d x} (ln (\frac{3 x}{2 x + 1}))

\int \frac{1}{( x + 2 ) ( x + 7 ) ( 2 x - 5 ) ( x + 1 ) ^{2}} d x

y = x e^{- 0.4 x}, x = 5, y = 0

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