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

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

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

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

\infty

Solution steps

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

x \to - 1 + lim (ln (x + 1)) = - \infty

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

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

Apply Infinity Property:

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

= \infty

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

x \to 3 + lim (\frac{7 x - 5}{x - 3})

x \to 4 lim (\frac{3 x - 1}{x - 4})

x \to 2 lim (3 x^{2} + 5)

x \to \frac{2 π}{3} lim (sin (x))

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