What is the limit as x approaches 0+of (ln(x))/(x-1) ?

The limit as x approaches 0+of (ln(x))/(x-1) is infinity

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limit as x approaches 0+of (ln(x))/(x-1)

x \to 0 + lim (\frac{ln ( x )}{x - 1})

\infty

Solution steps

x \to 0 + lim (\frac{ln ( x )}{x - 1})

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 +} ( ln ( x ) )}{lim _{x \to 0 +} ( x - 1 )}

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

x \to 0 + lim (x - 1) = - 1

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

Apply Infinity Property:

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

= \infty

x \to - 1 lim (\frac{x ^{2} - 2}{x ^{2} - 5 x - 6})

x \to \infty lim (\frac{x ^{2} - 9}{x \cdot ( x ^{2} + 1 )})

x \to \infty lim (\frac{x ^{2} - 5 x + 6}{x - 2})

x \to \infty lim (ln ((1 - \frac{3}{x})^{x}))

x \to 1 lim (3 x^{2} - 2 x)

What is the limit as x approaches 0+of (ln(x))/(x-1) ?
The limit as x approaches 0+of (ln(x))/(x-1) is infinity